{ From user Lonnie, Model Intro_to_statistical at Thu, Aug 21, 2008 11:01 AM~~
}
Softwareversion 4.1.1
{ System Variables with non-default values: }
{!40000|Att_contlinestyle Run: 0}
Typechecking := 1
Checking := 1
Saveoptions := 2
Savevalues := 0
Allwarnings := 0
{!40000|Att_contlinestyle Graph_primary_valdim: 1}
{!40000|Att_catlinestyle Graph_primary_valdim: 9}
{!40000|Att_contlinestyle Graph_pdf_valdim: 1}
{!40000|Att_catlinestyle Graph_prob_valdim: 9}
Askattribute Domain,Variable,Yes
Model Intro_to_statistical
Title: Intro to Statistical Functions
Description: Analytica User Group Webinar, 22 Aug 2008~
~
A statistical function is a function that process a data set containi~~
ng many sample points, computing a "statistic" that summarizes the da~~
ta. Simple examples are Mean and Variance, but more complex examples ~~
may return matrices or tables. In this talk, I'll review statistical ~~
functions that are built into Analytica. I'll describe several built-~~
in statistical functions such as Mean, SDeviation, GetFract, Pdf, Cdf~~
, and Covariance. I'll demonstrate how all built-in statistical funct~~
ions can be applied to historical data sets over an arbitrary index, ~~
as well as to uncertain samples (the Run index). I'll discuss how the~~
domain attribute should be utilized to indicate that numeric-valued ~~
data is discrete (such as integer counts, for example), and how vario~~
us statistical functions (e.g., Frequency, GetFract, Pdf, Cdf, etc) m~~
ake use of this information. In the process, I'll demonstrate numerou~~
s examples using these functions, such things as inferring sample cov~~
ariance or correlation matricies from data, quickly histogramming arb~~
itrary data and using the coordinate index setting to plot it, or usi~~
ng a weighted Frequency for rapid aggregation. ~
~
We'll also see how to create your own user-defined statistical functi~~
on, and some things to be careful of when creating UDFs that utilize ~~
statistical functions.~
~
Statistical functions also support weighted statistics, where each sa~~
mple point is assigned a different weight. I'll touch on this topic ~~
briefly as a seque into next week's webinar on importance sampling.
Author: Lonnie Chrisman~
Lumina Decision Systems
Date: Thu, Aug 21, 2008 8:14 AM
Saveauthor: Lonnie
Savedate: Thu, Aug 21, 2008 11:01 AM
Defaultsize: 48,24
Diagstate: 1,13,14,550,399,17
Windstate: 2,102,90,576,446
Fontstyle: Arial, 15
Fileinfo: 0,Model Intro_to_statistical,2,2,0,0,W:\Training\User Group ~~
Webinars\Intro to Statistical Functions.ANA
Module Statistical_function
Title: Statistical functions applied to historical data
Defaultsize: 48,24
Nodelocation: 104,96,1
Nodesize: 64,44
Diagstate: 1,338,39,550,391,17
Index Trading_date
Title: Trading Date
Definition: [37.623K,37.624K,37.625K,37.628K,37.629K,37.63K,37.631K,37~~
.632K,37.636K,37.637K,37.638K,37.639K,37.642K,37.643K,37.644K,37.645K~~
,37.646K,37.649K,37.65K,37.651K,37.652K,37.653K,37.656K,37.657K,37.65~~
8K,37.659K,37.66K,37.663K,37.664K,37.665K,37.666K,37.667K,37.671K,37.~~
672K,37.673K,37.674K,37.677K,37.678K,37.679K,37.68K,37.681K,37.684K,3~~
7.685K,37.686K,37.687K,37.688K,37.691K,37.692K,37.693K,37.694K,37.695~~
K,37.698K,37.699K,37.7K,37.701K,37.702K,37.705K,37.706K,37.707K,37.70~~
8K,37.709K,37.712K,37.713K,37.714K,37.715K,37.719K,37.72K,37.721K,37.~~
722K,37.723K,37.726K,37.727K,37.728K,37.729K,37.73K,37.733K,37.734K,3~~
7.735K,37.736K,37.737K,37.74K,37.741K,37.742K,37.743K,37.744K,37.747K~~
,37.748K,37.749K,37.75K,37.751K,37.754K,37.755K,37.756K,37.757K,37.75~~
8K,37.761K,37.762K,37.763K,37.764K,37.765K,37.769K,37.77K,37.771K,37.~~
772K,37.775K,37.776K,37.777K,37.778K,37.779K,37.782K,37.783K,37.784K,~~
37.785K,37.786K,37.789K,37.79K,37.791K,37.792K,37.793K,37.796K,37.797~~
K,37.798K,37.799K,37.8K,37.803K,37.804K,37.806K,37.807K,37.81K,37.811~~
K,37.812K,37.813K,37.814K,37.817K,37.818K,37.819K,37.82K,37.821K,37.8~~
24K,37.825K,37.826K,37.827K,37.828K,37.831K,37.832K,37.833K,37.834K,3~~
7.835K,37.838K,37.839K,37.84K,37.841K,37.842K,37.845K,37.846K,37.847K~~
,37.848K,37.849K,37.852K,37.853K,37.854K,37.855K,37.856K,37.859K,37.8~~
6K,37.861K,37.862K,37.863K,37.867K,37.868K,37.869K,37.87K,37.873K,37.~~
874K,37.875K,37.876K,37.877K,37.88K,37.881K,37.882K,37.883K,37.884K,3~~
7.887K,37.888K,37.889K,37.89K,37.891K,37.894K,37.895K,37.896K,37.897K~~
,37.898K,37.901K,37.902K,37.903K,37.904K,37.905K,37.908K,37.909K,37.9~~
1K,37.911K,37.912K,37.915K,37.916K,37.917K,37.918K,37.919K,37.922K,37~~
.923K,37.924K,37.925K,37.926K,37.929K,37.93K,37.931K,37.932K,37.933K,~~
37.936K,37.937K,37.938K,37.939K,37.94K,37.943K,37.944K,37.945K,37.947~~
K,37.95K,37.951K,37.952K,37.953K,37.954K,37.957K,37.958K,37.959K,37.9~~
6K,37.961K,37.964K,37.965K,37.966K,37.967K,37.968K,37.971K,37.972K,37~~
.973K,37.974K,37.975K,37.978K,37.98K,37.981K,37.982K,37.985K,37.987K,~~
37.988K,37.989K,37.992K,37.993K,37.994K,37.995K,37.996K,37.999K,38K,3~~
8.001K,38.002K,38.003K,38.007K,38.008K,38.009K,38.01K,38.013K,38.014K~~
,38.015K,38.016K,38.017K,38.02K,38.021K,38.022K,38.023K,38.024K,38.02~~
7K,38.028K,38.029K,38.03K,38.031K,38.035K,38.036K,38.037K,38.038K,38.~~
041K,38.042K,38.043K,38.044K,38.045K,38.048K,38.049K,38.05K,38.051K,3~~
8.052K,38.055K,38.056K,38.057K,38.058K,38.059K,38.062K,38.063K,38.064~~
K,38.065K,38.069K,38.07K,38.071K,38.072K,38.073K,38.076K,38.077K,38.0~~
78K,38.079K,38.08K,38.083K,38.084K,38.085K,38.086K,38.087K,38.09K,38.~~
091K,38.092K,38.093K,38.094K,38.097K,38.098K,38.099K,38.1K,38.101K,38~~
.104K,38.105K,38.106K,38.107K,38.108K,38.111K,38.112K,38.113K,38.114K~~
,38.115K,38.118K,38.119K,38.12K,38.121K,38.122K,38.125K,38.126K,38.12~~
7K,38.128K,38.129K,38.133K,38.134K,38.135K,38.136K,38.139K,38.14K,38.~~
141K,38.142K,38.143K,38.146K,38.147K,38.148K,38.149K,38.15K,38.153K,3~~
8.154K,38.155K,38.156K,38.157K,38.16K,38.161K,38.162K,38.163K,38.164K~~
,38.167K,38.168K,38.169K,38.17K,38.174K,38.175K,38.176K,38.177K,38.17~~
8K,38.181K,38.182K,38.183K,38.184K,38.185K,38.188K,38.189K,38.19K,38.~~
191K,38.192K,38.195K,38.196K,38.197K,38.198K,38.199K,38.202K,38.203K,~~
38.204K,38.205K,38.206K,38.209K,38.21K,38.211K,38.212K,38.213K,38.216~~
K,38.217K,38.218K]
Nodelocation: 104,48,1
Nodesize: 48,24
Numberformat: 2,DD,2,2,0,0,4,0,$,0,"ABBREV",0
{!40000|Att_previndexvalue: [37.623K,37.624K,37.625K,37.628K,37.629K,37.63K~~
,37.631K,37.632K,37.636K,37.637K,37.638K,37.639K,37.642K,37.643K~~
,37.644K,37.645K,37.646K,37.649K,37.65K,37.651K,37.652K,37.653K,37.656K~~
,37.657K,37.658K,37.659K,37.66K,37.663K,37.664K,37.665K,37.666K,37.667K~~
,37.671K,37.672K,37.673K,37.674K,37.677K,37.678K,37.679K,37.68K,37.681K~~
,37.684K,37.685K,37.686K,37.687K,37.688K,37.691K,37.692K,37.693K,37.694K~~
,37.695K,37.698K,37.699K,37.7K,37.701K,37.702K,37.705K,37.706K,37.707K~~
,37.708K,37.709K,37.712K,37.713K,37.714K,37.715K,37.719K,37.72K,37.721K~~
,37.722K,37.723K,37.726K,37.727K,37.728K,37.729K,37.73K,37.733K,37.734K~~
,37.735K,37.736K,37.737K,37.74K,37.741K,37.742K,37.743K,37.744K,37.747K~~
,37.748K,37.749K,37.75K,37.751K,37.754K,37.755K,37.756K,37.757K,37.758K~~
,37.761K,37.762K,37.763K,37.764K,37.765K,37.769K,37.77K,37.771K,37.772K~~
,37.775K,37.776K,37.777K,37.778K,37.779K,37.782K,37.783K,37.784K,37.785K~~
,37.786K,37.789K,37.79K,37.791K,37.792K,37.793K,37.796K,37.797K,37.798K~~
,37.799K,37.8K,37.803K,37.804K,37.806K,37.807K,37.81K,37.811K,37.812K~~
,37.813K,37.814K,37.817K,37.818K,37.819K,37.82K,37.821K,37.824K,37.825K~~
,37.826K,37.827K,37.828K,37.831K,37.832K,37.833K,37.834K,37.835K,37.838K~~
,37.839K,37.84K,37.841K,37.842K,37.845K,37.846K,37.847K,37.848K,37.849K~~
,37.852K,37.853K,37.854K,37.855K,37.856K,37.859K,37.86K,37.861K,37.862K~~
,37.863K,37.867K,37.868K,37.869K,37.87K,37.873K,37.874K,37.875K,37.876K~~
,37.877K,37.88K,37.881K,37.882K,37.883K,37.884K,37.887K,37.888K,37.889K~~
,37.89K,37.891K,37.894K,37.895K,37.896K,37.897K,37.898K,37.901K,37.902K~~
,37.903K,37.904K,37.905K,37.908K,37.909K,37.91K,37.911K,37.912K,37.915K~~
,37.916K,37.917K,37.918K,37.919K,37.922K,37.923K,37.924K,37.925K,37.926K~~
,37.929K,37.93K,37.931K,37.932K,37.933K,37.936K,37.937K,37.938K,37.939K~~
,37.94K,37.943K,37.944K,37.945K,37.947K,37.95K,37.951K,37.952K,37.953K~~
,37.954K,37.957K,37.958K,37.959K,37.96K,37.961K,37.964K,37.965K,37.966K~~
,37.967K,37.968K,37.971K,37.972K,37.973K,37.974K,37.975K,37.978K,37.98K~~
,37.981K,37.982K,37.985K,37.987K,37.988K,37.989K,37.992K,37.993K,37.994K~~
,37.995K,37.996K,37.999K,38K,38.001K,38.002K,38.003K,38.007K,38.008K,~~
38.009K,38.01K,38.013K,38.014K,38.015K,38.016K,38.017K,38.02K,38.021K~~
,38.022K,38.023K,38.024K,38.027K,38.028K,38.029K,38.03K,38.031K,38.035K~~
,38.036K,38.037K,38.038K,38.041K,38.042K,38.043K,38.044K,38.045K,38.048K~~
,38.049K,38.05K,38.051K,38.052K,38.055K,38.056K,38.057K,38.058K,38.059K~~
,38.062K,38.063K,38.064K,38.065K,38.069K,38.07K,38.071K,38.072K,38.073K~~
,38.076K,38.077K,38.078K,38.079K,38.08K,38.083K,38.084K,38.085K,38.086K~~
,38.087K,38.09K,38.091K,38.092K,38.093K,38.094K,38.097K,38.098K,38.099K~~
,38.1K,38.101K,38.104K,38.105K,38.106K,38.107K,38.108K,38.111K,38.112K~~
,38.113K,38.114K,38.115K,38.118K,38.119K,38.12K,38.121K,38.122K,38.125K~~
,38.126K,38.127K,38.128K,38.129K,38.133K,38.134K,38.135K,38.136K,38.139K~~
,38.14K,38.141K,38.142K,38.143K,38.146K,38.147K,38.148K,38.149K,38.15K~~
,38.153K,38.154K,38.155K,38.156K,38.157K,38.16K,38.161K,38.162K,38.163K~~
,38.164K,38.167K,38.168K,38.169K,38.17K,38.174K,38.175K,38.176K,38.177K~~
,38.178K,38.181K,38.182K,38.183K,38.184K,38.185K,38.188K,38.189K,38.19K~~
,38.191K,38.192K,38.195K,38.196K,38.197K,38.198K,38.199K,38.202K,38.203K~~
,38.204K,38.205K,38.206K,38.209K,38.21K,38.211K,38.212K,38.213K,38.216K~~
,38.217K,38.218K]}
Index Stock
Title: Stock
Definition: ['GOOG','MSFT','YHOO','ORCL','INTC','AAPL']
Nodelocation: 104,112,1
Nodesize: 48,24
{!40000|Att_previndexvalue: ['GOOG','MSFT','YHOO','ORCL','INTC','AAPL'~~
]}
Variable Stock_price
Title: Stock Price
Definition: Table(Trading_date,Stock)(~
467.59,29.86,25.61,17.51,20.35,83.8,~
483.26,29.81,26.85,17.68,21.17,85.66,~
487.19,29.64,27.74,17.64,21.1,85.05,~
483.58,29.93,27.92,17.86,21.01,85.47,~
485.5,29.96,27.58,17.82,21.03,92.56999999999999,~
489.46,29.66,28.7,17.77,21.52,97,~
499.72,30.7,29.2,17.39,21.92,95.8,~
505,31.21,29.45,17.5,22.13,94.62000000000001,~
504.28,31.16,29.29,17.3,22.3,97.09999999999999,~
497.28,31.1,29.05,17.52,21.04,94.95,~
487.83,31,28.12,17.12,20.65,89.06999999999999,~
489.75,31.11,27.64,17.27,20.82,88.5,~
480.84,30.72,27.42,17,20.79,86.79000000000001,~
479.05,30.74,26.96,17.12,20.55,85.7,~
499.07,31.09,28.94,17.14,20.84,86.7,~
488.09,30.45,28.21,16.98,20.6,86.25,~
495.84,30.6,28.04,17.15,20.53,85.38,~
492.47,30.53,27.87,17.27,20.89,85.94,~
494.32,30.48,28.04,17.16,20.93,85.55,~
501.5,30.86,28.31,17.16,20.96,85.73,~
481.75,30.56,28.35,17.05,21.11,84.74,~
481.5,30.19,28.77,17.42,21.23,84.75,~
467.16,29.61,28.56,17.16,21.28,83.94,~
471.48,29.51,29.35,17.02,21.31,84.15000000000001,~
470.01,29.37,29.89,16.91,21.51,86.15000000000001,~
471.03,29.26,30.08,16.71,21.36,86.18000000000001,~
461.89,28.98,29.74,16.7,21.03,83.27,~
458.29,28.94,29.17,16.65,20.8,84.88,~
459.1,29.01,29.56,16.62,20.87,84.7,~
465.93,29.4,30.66,16.77,21.14,85.3,~
461.47,29.46,31.25,16.91,21.31,85.20999999999999,~
469.94,28.74,31.91,16.7,21.23,84.83,~
472.1,28.83,32.01,16.98,21.18,85.90000000000001,~
475.86,29.35,31.65,17.2,20.88,89.2,~
475.85,29.39,31.6,17.27,20.97,89.51000000000001,~
470.62,28.9,32.1,16.82,20.76,89.06999999999999,~
464.93,29.07,32.11,16.82,20.85,88.51000000000001,~
448.77,27.87,30.95,16.29,20.03,83.93000000000001,~
449.45,28.17,30.86,16.43,19.86,84.61,~
448.23,28.09,30.86,16.77,19.59,87.06,~
438.68,27.76,30.42,16.71,19.22,85.41,~
440.95,27.55,30.31,16.37,19.11,86.31999999999999,~
457.55,27.83,30.8,16.88,19.4,88.19,~
455.64,27.61,30.39,16.49,19.12,87.72,~
454.72,27.32,30.71,16.69,19.23,88,~
452.96,27.29,29.12,16.63,19.1,87.97,~
454.75,27.44,29.99,17.07,19.48,89.87000000000001,~
443.03,26.72,29.56,16.65,19.12,88.40000000000001,~
448,27.4,29.86,16.88,19.23,90,~
446.19,27.28,30.06,16.72,19.14,89.56999999999999,~
440.85,27.33,29.88,16.7,19.15,89.59,~
447.23,27.83,30.03,17.18,19.11,91.13,~
445.28,27.84,30.33,17.55,18.99,91.48,~
456.55,28.52,31.29,18.17,19.34,93.87000000000001,~
462.04,28.27,31.26,18.49,19.16,93.95999999999999,~
461.83,28.02,31.36,18.24,19.27,93.52,~
465,28.22,31.66,18.39,19.29,95.84999999999999,~
463.62,27.72,31.55,18.49,19.06,95.45999999999999,~
461.88,27.64,31.41,18.17,18.86,93.24,~
460.92,27.75,31.34,18.16,19.09,93.75,~
458.16,27.87,31.29,18.13,19.13,92.91,~
458.53,27.74,31.28,18.14,19.13,93.65000000000001,~
472.6,27.87,31.72,18.36,19.31,94.5,~
471.02,28.5,31.62,18.56,19.38,94.27,~
471.51,28.55,31.96,18.67,19.58,94.68000000000001,~
468.21,28.57,31.64,18.57,20.1,93.65000000000001,~
466.5,28.4,31.69,18.85,20.68,94.25,~
464.53,28.11,31.17,18.59,20.47,92.59,~
467.39,28.54,31.21,18.7,20.5,92.19,~
466.29,28.61,31.41,18.63,20.46,90.24,~
474.27,28.73,31.61,18.9,20.69,91.43000000000001,~
472.8,28.85,32.09,18.89,20.98,90.34999999999999,~
476.01,28.6,28.31,18.73,21.35,90.40000000000001,~
471.65,28.69,27.51,18.76,21.81,90.27,~
482.48,29.02,27.46,19,22.16,90.97,~
479.08,28.78,27.88,18.94,21.91,93.51000000000001,~
477.53,28.79,28.02,18.82,21.94,93.24,~
477.99,28.99,28.06,18.9,22.26,95.34999999999999,~
481.18,29.1,28.49,18.95,22.09,98.84,~
479.01,30.12,28.34,19.1,21.87,99.92,~
471.38,29.94,28.04,18.8,21.5,99.8,~
469,30.4,27.73,18.59,21.8,99.47,~
465.78,30.61,28.12,18.86,21.93,100.39,~
473.23,30.97,28.18,19.02,21.74,100.4,~
471.12,30.56,30.98,19.03,21.9,100.81,~
467.27,30.71,30.38,19.05,21.96,103.92,~
466.81,30.75,30.41,18.95,22.15,105.06,~
469.25,30.78,30.22,18.83,22.47,106.88,~
461.47,30.58,29.7,18.49,22.21,107.34,~
466.74,30.89,30.05,18.98,22.28,108.74,~
461.78,30.97,29.31,18.94,22.12,109.36,~
458,30.9,28.81,18.84,22.01,107.52,~
472.61,31.07,29.21,18.99,22.18,107.34,~
470.96,30.98,28.57,19.05,22.23,109.44,~
470.32,30.83,29.75,19.25,22.7,110.02,~
470.6,31.05,29.35,19.32,22.63,111.98,~
475.86,30.69,28.92,19.37,22.99,113.54,~
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498.3,27.69,19.73,22.77,24.01,175.39,~
490.5,27.32,19.42,22.56,23.59,173.53,~
485,27.29,19.17,22.66,23.39,175.84~
)
Nodelocation: 224,48,1
Nodesize: 48,24
Defnstate: 2,84,50,416,303,0,MIDM
Valuestate: 2,196,139,543,397,0,MIDM
Graphsetup: {!40000|Att_graphvaluerange Stock_price:1,,,,0}
Reformdef: [Stock,Trading_date]
Reformval: [Trading_date,Stock]
Numberformat: 2,F,4,2,0,1,4,1,$,0,"ABBREV",0
Variable Daily_change
Title: Daily change
Definition: if @Trading_date=1 then 0 else Stock_price / Stock_price[@~~
Trading_date=@Trading_date-1] - 1
Nodelocation: 336,48,1
Nodesize: 48,24
Valuestate: 2,23,78,655,507,1,MIDM
Graphsetup: {!40000|Att_contlinestyle Graph_primary_valdim:4}
Reformval: [Trading_date,Undefined]
Numberformat: 2,%,4,2,0,0,4,0,$,0,"ABBREV",0
{!40000|Att_xrole: 30-Dec-1903}
{!40000|Att_yrole: 29-Dec-1903}
{!40000|Att_coordinateindex: Stock}
Variable Mean_change
Title: mean change
Definition: mean( Daily_change, Trading_date, w:wt )
Nodelocation: 224,112,1
Nodesize: 48,24
Reformval: [Wt_type,Stock]
Variable Sd_change
Title: sd change
Definition: SDeviation(Daily_change,Trading_date)
Nodelocation: 336,112,1
Nodesize: 48,24
Variable Histo_change
Title: histo change
Definition: pdf(Daily_change,Trading_date)
Nodelocation: 448,112,1
Nodesize: 48,24
Valuestate: 2,184,194,537,409,1,MIDM
Reformval: [Sys_localindex('STEP'),Stock]
{!40000|Att_resultslicestate: [Densityindex,2,Stock,1,Sys_localindex(~~
'STEP'),1]}
{!40000|Att_coordinateindex: Densityindex}
Variable Correlation_change
Title: Correlation change
Definition: Correlation( Daily_change, Daily_change[Stock=Stock2], Tra~~
ding_date )
Nodelocation: 224,168,1
Nodesize: 48,24
Valuestate: 2,496,235,515,221,0,MIDM
Reformval: [Stock,Stock2]
Index Stock2
Title: Stock2
Definition: CopyIndex(Stock)
Nodelocation: 104,176,1
Nodesize: 48,24
Variable Cov_change
Title: Cov change
Definition: Covariance( Daily_change, Daily_change[Stock=Stock2], Trad~~
ing_date, w:wt )
Nodelocation: 336,176,1
Nodesize: 48,24
Valuestate: 2,392,301,550,215,0,MIDM
Reformval: [Stock,Stock2]
Library Multivariate_distrib
Title: Multivariate Distributions
Description: A library of multivariate distributions.~
~
In a multivariate distribution, each sample is a vector. This vector~~
is identified by an index, identified by the I parameter of the func~~
tions in this library. A Mid value from a distribution function will~~
therefore be indexed by I, whlie a Sample from a distribution functi~~
on is indexed by both I and Run. These distribution functions can al~~
so be used from within the Random function to generate a single monte~~
-carlo sample, which will be indexed by I.~
~
This library also contains functions for generating correlated distri~~
butions. Correlate_with, for example, allows you to generate a univa~~
rite distribution with an arbitrary marginal distribution that has a ~~
specified rank correlation with an arbitrary reference distribution. ~~
Several functions may be used for generating serial correlations, w~~
here each distribution along an index is correlated with the previous~~
point along that index.
Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems~
~
With contributions by:~
John Bowers, US FDA.~
Max Henrion, Lumina Decision Systems
Date: Fri, Aug 01, 2003 7:12 PM
Saveauthor: Lonnie
Savedate: Wed, Jun 11, 2008 9:46 AM
Defaultsize: 48,24
Nodelocation: 112,256,0
Nodesize: 64,24
Nodeinfo: 1,1,1,1,1,1,0,0,0,0
Diagstate: 1,42,10,649,1009,17
Windstate: 2,401,199,483,316
Fontstyle: Arial, 15
Function Wishart( cv : Number[I,J,Run] ; n :positive ; I,J : Index ; ~
singleSampleMethod : optional hidden scalar)
Title: Wishart(cv,n,I,J)
Description: Suppose you sample N samples from a Gaussian(0,cv,I,J) di~~
stribution, X[I,R]. (R is the index that indexes each sample, R:=1..~~
N). The Wishart distribution describes the distribution of sum( X * ~~
X[I=J], R ). This matrix is dimensioned by I and J and is called the~~
scatter matrix. ~
~
A sample drawn from the Wishart is therefore a sample scatter matrix.~~
If you divide that sample by (N-1), you have a sampled covariance m~~
atrix. ~
~
If you compute a sample covariance matrix from data, and then want to~~
use this in your model, if you just use it directly, you'll be ignor~~
ing sampling error. That may be insignificant of N is large. Otherw~~
ise, you may want to use:~
Wishart( SampleCV, N, I, J) / (N-1)~
instead of just SampleCV in your model. The extended variance will ~~
account for the uncertainty from the finite sample size that was used~~
to obtain your sample CV.~
~
If you can express a prior probability on covariances in the form of ~~
an InvertedWishart distribution, then the posterior distribution, aft~~
er having computed the sample covariance matrix (assumed to be drawn,~~
by nature, from a Wishart), is also an InvertedWishart.
Definition: var T := if i0~
Each sample of a Dirichlet distribution produces a random vector whos~~
e elements sum to 1. It is commonly used to represent second order p~~
robability information.~
~
The Dirichlet distribution has a density given by ~
k * Product( X^(alpha-1), I)~
where k is a normalization factor equal to~
GammaFn( sum(alpha,I )) / Sum(GammaFn(alpha),I)~
~
The parameters, alpha, can be interpreted as observation counts. The~~
mean is given by the relative values of alpha (normalized to 1), but~~
the variance narrows as the alphas get larger, just as your confiden~~
ce in a distribution would narrow as you get more samples.~
~
The Dirichlet lends itself to easy Bayesian updating. If you have a ~~
prior of alpha0, and you observe N
Definition: var a:=Gamma(alpha,singleSampleMethod:singleSampleMethod);~~
~
a/sum(a,I)
Nodelocation: 272,120,1
Nodesize: 58,16
Windstate: 2,26,18,624,485
Paramnames: alpha,I,Over
Function Binormal(MeanVec :numeric[I,Run]; Sdeviations : positive[I,Ru~~
n]; I:IndexType; correlationCoef : numeric[Run];~
Over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar)
Title: BiNormal (m, s, i, c )
Description: A 2-D Normal (or Bi-variate Gaussian) distribution with t~~
he indicated individual standard deviations (>0) and the indicated co~~
rrelation coefficient. The index, I, must have exactly 2 elements, S~~
deviations must be indexed by I.
Definition: if size(I)<>2 then ~
Error("Index to BiNormal must have 2 elements")~
else begin~
var s := product(Sdeviations,I) * correlationCoef;~
Index J:=CopyIndex(I);~
Gaussian( meanVec, If I<>J Then s else Sdeviations^2, I,J,~
singleSampleMethod: singleSampleMethod )~
end
Nodelocation: 288,72,1
Nodesize: 78,16
Windstate: 2,2,24,525,540
Paramnames: MeanVec,Sdeviations,I,correlationCoef,Over
Function Multinomial(N:Positive ; theta:NonNegative ; I : IndexType;~
Over : ... optional atomic ;~
singleSampleMethod : hidden optional scalar )
Title: Multinomial (n, theta, i )
Description: Returns the Multinomial Distribution.~
~
The multinomial distribution is a generalization of the Binomial dist~~
ribution to N possible outcomes. For example, if you were to roll a ~~
fair die N times, an outcome would be the number of times each of the~~
six numbers appears. Theta would be the probability of each outcome~~
, where sum(theta,I)=1, and index I is the list of possible outcome. ~~
If theta doesn't sum to 1, it is normalized.~
~
Each sample is a vector indexed by I indicating the number of times t~~
he corresponding outcome (die number) occurred during that sample poi~~
nt. Each sample will have the property that sum( result, I ) = N.
Definition: var z := n;~
var k := size(I);~
~
var j:=cumulate(1,I) in I do begin~
Index I2 := j..k;~
var theta2 := Slice(theta,I,I2); /* unnormalized sub-process */~
var p := theta2/sum(theta2, I2);~
p := if IsNan(p) then 0 else p;~
var xj := Binomial(z,p[I2=j],~
singleSampleMethod:singleSampleMethod);~~
~
z := z - xj;~
xj~
end~
Nodelocation: 117,120,1
Nodesize: 85,16
Windstate: 2,75,167,476,522
Paramnames: N,theta,I,Over
Function Correlate_dists(dists : Context[I,RunIndex] ; rankcorrs : num~~
eric array[I,J] ; ~
I,J : IndexType;~
RunIndex : optional Index = Run )
Title: Correlate Dists (d, rc, i, j )
Description: Reorders the samples in dists so as to match the desired~~
rank correlations between distributions as closely as possible. Ran~~
kCorrs must be positive definite, and the diagonal should contain all~~
ones.~
~
The result will be distributions having the same margins as the origi~~
nal input, but with rank correlations close to those of the rankcorrs~~
matrix.
Definition: if not IsSampleEvalMode and Handle(RunIndex)=Handle(Run) T~~
hen~
dists {Mid mode}~
Else begin~
var u := if Handle(RunIndex)=Handle(run) ~
Then Sample(Gaussian(0,rankcorrs,I,J))~
Else Random(Gaussian(0,rankcorrs,I,J),Over:RunIndex);~
var dsort := sortIndex(dists,RunIndex);~
var urank := Rank(u,RunIndex);~
dists[RunIndex=dsort[RunIndex=urank]]~
end
Nodelocation: 136,392,1
Nodesize: 100,16
Windstate: 2,301,193,494,399
Paramnames: dists,rankcorrs,I,J,RunIndex
Function Correlate_with( S, ref : Context[RunIndex] ; rc : scalar ; ~
RunIndex : optional Index = Run )
Title: Correlate With (s, ref, rc )
Description: Reorders the samples of S so that the result is correlate~~
d with the reference sample with a rank correlation close to rankcorr~~
. ~
~
Example: To generate a logNormal distribution that is highly correlat~~
ed with Ch1, use, e.g.,: Correlate_With( LogNormal(2,3), Ch1, 0.8 )~
~
Note: This achieves a given unweighted rank correlation. If you have~~
a non-default SampleWeighting of points, the weighted rank correlato~~
n may differ.
Definition: if IsSampleEvalMode or Handle(runIndex)<>Handle(Run) Then ~~
begin~
Index q := 1..2;~
var u := If Handle(RunIndex)=Handle(Run) ~
Then binormal( 0, 1, q, rc )~
Else Random(binormal(0,1,q,rc),Over:RunIndex);~
var rrank := Rank(ref,RunIndex);~
var u1sort := sortIndex(u[q=1],RunIndex);~
var u2rank := Rank(u[q=2],RunIndex);~
var ssort := sortIndex(S,RunIndex);~
S[RunIndex=ssort[RunIndex=u2rank[RunIndex=~
u1sort[Ru~~
nIndex=rrank]]]]~
end ~
else {mid mode}~
S
Nodelocation: 128,312,1
Nodesize: 96,16
Windstate: 2,205,170,545,485
Paramnames: S,ref,rc,RunIndex
Function Uniformspherical(I : IndexType ; R : optional Numeric[I,Run] ~~
;~
Over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Uniform Spherical (i, r )
Description: Generates points uniformly on a sphere (or circle or hype~~
rsphere).~
Each sample generated is indexed by I -- so if I has 3 elements, the ~~
points will lie on a sphere.~
~
The mid value is a bit strange here since there isn't really a median~~
that lies on the sphere. Obviously the center of the sphere is the ~~
middle value, but that isn't in the allowable range. So, an arbitrar~~
y point on the sphere is used.
Definition: if IsNotSpecified(R) then R:=1;~
var u := Normal(0,1,over:I,~
singleSampleMethod:singleSampleMethod); ~
var d := sqrt( sum(u^2,I) );~
ifall d=0 and @I then R/sqrt(size(I)) else r*u/d
Nodelocation: 328,168,1
Nodesize: 86,16
Windstate: 2,151,227,476,424
Paramnames: I,R,Over
Function Multiuniform(corr : Numeric[I,J,Run] ; I,J : IndexType ; lb,u~~
b : optional Numeric[I,J,Run] ;~
Over : ... optional atomic ;~
singleSampleMethod : hidden optional scalar )
Title: MultiUniform ( c, i, j, lb, ub )
Description: The multi-variate uniform distribution.~
Generates vector samples (indexed by I) such that each component has ~~
a uniform marginal distribution, and such that each component have th~~
e pair-wise correlations given by corr. Indexes I and J must have th~~
e same number of elements, corr needs to be symmetric and must obey a~~
certain semidefinite condition (namely that the transformed matrix [~~
2*sin(30*cov) ] is positive semidefinite. In most cases, this rough~~
ly the same as corr being, or not being, positive semidefinite). Lb ~~
and ub can be used to specify upper and lower bounds, either for all ~~
components, or individually if these bounds are indexed by I. If lb ~~
& ub are omitted, each component will have marginal Uniform(0,1).~
~
The correlation specified in corr is true sample correlation - not ra~~
nk correlation. ~
~
The transformation here is based on:~
* Falk, M. (1999), "A simple approach to the generation of uniformly ~~
distributed random variables with prescribed correlations," Comm. in ~~
Stats - Simulation and Computation 28: 785-791.
Definition: if IsNotSpecified(lb) then lb:=0;~
if IsNotSpecified(ub) then ub := 1;~
var R := if I=J then 1 else 2*sin(30*corr);~
var g := Gaussian(0,R,I,J,~
singleSampleMethod:singleSampleMethod);~~
~
Cumnormal( g ) * (ub-lb) + lb
Nodelocation: 132,168,1
Nodesize: 100,16
Windstate: 2,67,106,608,611
Paramnames: corr,I,J,lb,ub,Over
Module Depricated_multi_var
Title: Depricated multi-variate stuff
Description: Functions found in this module are here for legacy reason~~
s. They existed in older versions of the Multivariate library, but h~~
ave been become obsolete for whatever reason.
Author: Lonnie
Date: Mon, Apr 30, 2007 3:49 PM
Defaultsize: 48,24
Nodelocation: 80,944,1
Nodesize: 56,32
Function Samplecovariance(X ; I : Index ; J : optional Index ; R : Ind~~
ex)
Title: Sample Covariance
Description: This function is obsolete. In Analytica 4.0, the builtin~~
function Variance can be used to compute a covariance matrix. The e~~
quivalent of this function would be: Variance( X, R, CoVarDim:I, CoV~~
arDim2:J ).~
~
Returns a covariance matrix based on the sampled data, X, indexed by ~~
I and R. (I is the dimensionality of X, R corresponds to the samples~~
). The result will be indexed by I and J -- supply J to be the same ~~
length as I.~
~
Note that the mean is simply Average(X,R), and doen't warrant a separ~~
ate function.
Definition: var I2 := if IsNotSpecified(J) ~
Then (Index K/((identifier of I)&"2") := I do VarTerm(K~~
)) ~
Else VarTerm(J);~
var Z:=X-Average(X,R);~
var Zt := Z[@I=@I2];~
Sum(Z*Zt,R)/(size(R)-1)
Nodelocation: 80,48,1
Nodesize: 48,24
Windstate: 2,222,299,476,297
Paramnames: X,I,J,R
Function Samplecorrelation(X : array[I,R] ; I,J,R : IndexType)
Title: sample correlation
Description: This function is obsolete. A covariance matrix can be co~~
mputed in Analytica 4.0+ using the built-in function Correlation. Th~~
e equivalent of this function is Correlation(X,X[@I=@J],R).~
~
Returns a correlation matrix based on data in X, where each data poin~~
t is a vector indexed by I, and the entries in the correlation matrix~~
are the pair-wise correlations of the columns of data. A second ind~~
ex, J, of size identical to I, is required in order to index the 2-di~~
mensional result.
Definition: var z:=x-average(x,R);~
var zt := slice(z,I,cumulate(1,J));~
sum(z*zt,R) / sqrt(sum(z^2,R) * sum(zt^2,R))~
Nodelocation: 208,48,1
Nodesize: 48,24
Windstate: 2,70,24,523,377
Paramnames: X,I,J,R
Close Depricated_multi_var
Text Multvar_te1
Description: Parametric Multivariate Distributions
Nodelocation: 160,40,-1
Nodesize: 136,12
Text Multvar_te2
Description: Creating an array of mutually correlated distributions:
Nodelocation: 232,368,-1
Nodesize: 200,16
Text Multvar_te3
Description: Creating a single univariate distribution correlated wit~~
h another existing dist:
Nodelocation: 296,280,-1
Nodesize: 268,12
Function Normal_correl(m, s, r, y: Numeric ;~
over : optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Normal_correl(m, s, r, y)
Description: Generates a normal distribution with mean m, standard dev~~
iation s, and correlation r with normally distributed value y. In a ~~
deterministic context, it will return m.~
~
If y is not normally distributed, the result will also not be normal,~~
and the correlation will be approximate. It generalizes appropriatel~~
y if any of the parameters are arrays:The result array will have the ~~
union of the indexes of the parameters.
Definition: IF r<-1 OR r>1 THEN Error('Correlation parameter r in func~~
tion Normal_correl(m, s, r, y) is outside the expected range [-1, 1].~~
');~
IFOnly IsSampleEvalMode ~
THEN m + s * (Sqrt(1-r^2) ~
* Normal(Sameindexes( 0, m ), Sameindexes( 1,~~
s ),~
singleSampleMethod:singleSampl~~
eMethod ) ~
+ r * (y - Mean(y))/Sdeviation(y))~
ELSE m
Nodelocation: 352,312,1
Nodesize: 108,16
Windstate: 2,102,90,503,416
Paramnames: m,s,r,y,over
Module Multivariate_interna
Title: Multivariate Internal Functions
Author: Lonnie
Date: Tue, May 01, 2007 9:29 PM
Defaultsize: 48,24
Nodelocation: 200,944,1
Nodesize: 52,32
Function Sameindexes(x, y)
Title: SameIndexes(x,y)
Description: Returns an array with the same indexes as y, and value x ~~
in each cell.
Definition: IF y=y THEN x ELSE x
Nodelocation: 120,64,1
Nodesize: 80,20
Paramnames: x,y
Close Multivariate_interna
Function Multinormal(m, s: Numeric; cm: ArrayType[i, j,Run]; i , j: In~~
dexType ;~
Over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Multinormal(m,s,c,i,j)
Description: A multi-variate normal (or Gaussian) distribution with me~~
an m, standard deviation s, and correlation matrix cm. m and s may ~~
be scalar or indexed by i. cm must be symmetric, positive-definite, a~~
nd indexed by i & j, which must be the same length.~
~
Multinormal uses a correlation matrix. Compare with Gaussian, which ~~
also defines a multi-variate normal but which uses a covariance matri~~
x.
Definition: Gaussian(m,cm*s*s[@i=@j],i,j,over,singleSampleMethod)
Nodelocation: 472,72,1
Nodesize: 84,16
Windstate: 2,391,248,512,343
Paramnames: m,s,cm,i,j,Over
Text Multvar_te4
Description: Reshaped distributions:
Nodelocation: 136,448,-1
Nodesize: 100,16
Function Dist_reshape(x : Numeric[R] ; newdist : all Numeric[R] ; ~
R : optional Index = Run )
Title: Dist_reshape(x, newdist)
Description: Reshapes the probability distribution of uncertain quanti~~
ty x so that it has the same marginal probability distribution (i.e, ~~
same set of sample values) as newdist, but retains the same ranks as ~~
x. Thus:~
Rank(Sample(x), Run) ~
= Rank(Sample(Reshape_dist(x, y)), Run)~
In a Mid context, it simply returns the mid value of newdist, with an~~
y indexes of x.~
~
The result retains any rank correlations that x may have with other p~~
redecessor variables. So, the rank-order correlation between a third~~
variable z and x will be the same as the rank-order correlation betw~~
een z and a reshaped version of x, i.e.~
RankCorrel(x, z) = RankCorrel(Reshape_Dist(x, y), z)~
~
The operation may optionally be applied along an index other than Run~~
.
Definition: IFOnly IsSampleEvalMode or Handle(R)<>Handle(Run) THEN BEG~~
IN~
VAR dsort := SortIndex(newdist, Run);~
VAR xranks := Rank(x, Run);~
newdist[Run = dsort[Run=xranks]]~
END~
ELSE newdist * (x=x)
Nodelocation: 152,472,1
Nodesize: 116,16
Windstate: 2,102,90,646,469
Paramnames: x,newdist,R
Text Multvar_te5
Description: Arrays with serial correlation
Nodelocation: 208,532,-1
Nodesize: 168,12
Function Normal_serial_correl(m, s, r: Numeric; i: IndexType ;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Normal_serial_correl(m,s,r,i)
Description: Generates an array over index i of normal distributions w~~
ith mean m, standard deviation s, and correlation r between successiv~~
e values over index i. You can give each distribution a different m~~
ean and/or standard deviation if m and/or s are arrays indexed by i. ~~
If r is indexed by i, r[i=k] specifies the correlation between result~~
[i=k] and result[i=k-1]. (Then the first correlation, slice(r, i, 1)~~
is ignored.)
Definition: Var x := Normal(0, 1,singleSampleMethod:singleSampleMethod~~
);~
(FOR j := i DO ~
x := Normal_correl( 0, 1, r[i = j],x,~
singleSampleMethod:singleSampl~~
eMethod ) ) ~
* s + m
Nodelocation: 160,560,1
Nodesize: 120,16
Windstate: 2,353,325,540,383
Paramnames: m,s,r,i,over
Function Normal_additive_gro(x, m, s, r: Numeric; i: IndexType ;~
over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Normal_additive_gro(x,m,s,r,i)
Description: Adds a normally distributed percent growth g with mean m ~~
and standard deviation s to x for each value of index i. The growth g~~
for each i has serial correlation r with g for i-1.
Definition: x *( 1 + Cumulate(Normal_serial_correl(m, s, r, i,~
singleSampleMethod:singleSampleMethod), i~~
))
Nodelocation: 159,600,1
Nodesize: 119,16
Windstate: 2,102,90,519,306
Paramnames: x,m,s,r,i,over
Function Normal_compound_gro(x, m, s, r: Numeric; t: IndexType ;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Normal_compound_gro(x,m,s,r,t)
Description: An array of values over time index t, starting from with ~~
value x, and with compound growth applied for each time interval, wit~~
h normal uncertainty with mean m and standard deviation s The growth~~
g for each i has correlation r with g for i-1.
Definition: x * Cumproduct(IF t = Slice(t, 1) THEN 1 ELSE Normal_seria~~
l_correl(m, s, r, t, singleSampleMethod:singleSampleMethod ) + 1, t)~~
Nodelocation: 159,640,1
Nodesize: 119,16
Windstate: 2,102,90,529,366
Paramnames: x,m,s,r,t,over
Function Dist_serial_correl(x; r; i: IndexType ;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Dist_serial_correl(x,r,i)
Description: Generates an array y over index i where each y[i] has a m~~
arginal distribution identical to x, and serial rank correlation of ~~
r with y[i-1]. If x is indexed by i, each y[i] has the same margin~~
al distribution as x[i], but with samples reordered to have the speci~~
fied rank correlation r between successive values. If r is indexed b~~
y i, r[i=k] specifies the rank correlation between y[i=k] and y[i=k-1~~
]. Then the first correlation, r[i=1], is ignored.~
~
In Mid context, it returns Mid(x).~
~
Note: The result retains no probabilistic dependence on x.
Definition: Dist_reshape(Normal_serial_correl( 0, 1, r, i, singleSampl~~
eMethod:singleSampleMethod ), x)
Nodelocation: 408,560,1
Nodesize: 120,16
Windstate: 2,302,78,477,447
Paramnames: x,r,i,over
Function Dist_additive_growth(x, g, r: Numeric; i: IndexType;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Dist_additive_growth(x,g,r,i)
Description: Generates an array of values over index i, with the first~~
equal to x, and successive values adding an uncertain growth with pr~~
obability distribution g, and serial correlation r between growth[i =~~
k] and growth[i=k-1]. x, g, and r each may be indexed by i if you w~~
ant them to vary over i.
Definition: x + Cumulate(Dist_serial_correl( g, r, i, singleSampleMeth~~
od : singleSampleMethod), i)
Nodelocation: 407,600,1
Nodesize: 119,16
Windstate: 2,102,90,506,300
Paramnames: x,g,r,i,over
Function Dist_compound_growth(x, g, r; i: IndexType ;~
over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Dist_compound_growth(x,g,r,i)
Description: Starts with x and applies a compound growth g for each va~~
lue of index i. The growth g for each i has correlation r with g for ~~
i-1.
Definition: x * Cumproduct(~
IF i = Slice(i, 1) THEN 1 ~
ELSE (Dist_serial_correl( g, r, i, ~
singleSampleMethod:singleSampleMe~~
thod ) + 1)~
, i)
Nodelocation: 407,640,1
Nodesize: 119,16
Windstate: 2,102,90,489,307
Paramnames: x,g,r,i,over
Text Multvar_te6
Description: Distributions on Linear Regression coefficients
Nodelocation: 296,688,-1
Nodesize: 256,12
Function Regressionnoise( Y : Numeric[I,Run] ; B : Numeric[I,K,Run] ; ~~
I,K : Index; C : optional Numeric[K,Run] )
Title: RegressionNoise(Y,B,I,K,C)
Description: When you have data, Y[I] and B[I,K], generated from an un~~
derlying model with unknown coefficients C[k] and S of the form:~
~
Y = Sum( C*B, I) + Normal(0,S)~
~
This function computes an estimate for S. ~
~
When using in conjunction with RegressionDist, it is most efficient t~~
o provide the optional parameter C to both routines, where C is the e~~
xpected value of the regression coefficients, obtained from calling R~~
egression(Y,B,I,K). Doing so avoids an unnecessary call to the built~~
in Regression function.
Definition: if IsNotSpecified(C) Then C := Regression(Y,B,I,K);~
Var resid := Y - Sum(C*B,K);~
sqrt( Sum(resid^2,I) / (size(I)-size(K)) );~
Nodelocation: 384,736,1
Nodesize: 104,20
Windstate: 2,332,211,498,542
Paramnames: Y,B,I,K,C
Function Regressionfitprob( Y : Numeric[I,Run] ; B : Numeric[I,K,Run] ~~
; I,K : Index; C : optional Numeric[K,Run] ; ~
S : optional Numeric[I,Run] )
Title: RegressionFitProb(Y,B,I,K,C)
Description: Once you've obtained regression coefficients C (indexed b~~
y K) by calling the Regression function, this function returns the pr~~
obability that a fit this poor would occur by chance, given the assum~~
ption that the data was generated by a process of the form:~
~
Y = Sum( C*B,K) + Normal(0,S)~
~
If this result is very close to zero, it probably indicates that the ~~
assumption of linearity is bad. If it is very close to one, then it ~~
validates the assumption of linearity.~
~
This is not a distribution function - it does not return a sample whe~~
n evaluated in Sample mode. However, it does complement the multivar~~
iate RegressionDist function also included in this library.~
~
To use, first call the Regression function, then you must either know~~
the measurement knows a priori, or obtain it using the RegressionNoi~~
se function.~
~
Var E_C := Regression(Y,B,I,K);~
Var S := RegressionNoise(Y,B,I,K,C);~
Var PrThisPoor := RegressionFitProb(Y,B,I,K,E_C,S)
Definition: if IsNotSpecified(C) then C:=Regression(Y,B,I,K);~
if IsNotSpecified(S) then S:=RegressionNoise(Y,B,I,K);~
var resid := Y - sum(C*B,K);~
var n := size(I);~
var chi2 := sum( resid^2 / Mean(S)^2, I);~
GammaI( n/2 - 1, chi2/2 )
Nodelocation: 152,800,1
Nodesize: 112,20
Windstate: 2,287,69,586,548
Paramnames: Y,B,I,K,C,S
Close Multivariate_distrib
Chance Simulated_change
Title: Simulated change
Definition: Gaussian( Mean_change, Cov_change, Stock, Stock2, Over:Fut~~
ure_date )
Nodelocation: 248,256,1
Nodesize: 48,24
Valuestate: 2,241,64,546,349,0,CONF
Graphsetup: Statsselect:[1, 1, 1, 1, 1, 1, 1, 1 ]~
{!40000|Att_contlinestyle Run:4}
Reformval: [Undefined,Undefined,Undefined,Undefined,1,2]
{!40000|Att_xrole: 30-Dec-1903}
{!40000|Att_yrole: 29-Dec-1903}
{!40000|Att_coordinateindex: Stock}
Index Future_date
Title: Future date
Definition: DateAdd( MakeDate(2008,8,21), 0..200, "wd" )
Nodelocation: 96,328,1
Nodesize: 48,24
Aliases: Alias Future_date1
Numberformat: 2,DD,2,2,0,0,4,0,$,0,"ABBREV",0
Variable Simulated_prices
Title: Simulated prices
Definition: Stock_price[@Trading_date=size(Trading_date)] * CumProduct~~
( 1+Simulated_change, Future_date )
Nodelocation: 248,320,1
Nodesize: 48,24
Valuestate: 2,185,184,821,432,0,MIDM
Aliases: Alias Simulated_prices1
Reformval: [Future_date,Stock]
{!40000|Att_resultslicestate: [Stock,6,Wt_type,1,Future_date,1]}
Variable Wt
Title: wt
Definition: Determtable(Wt_type)(~
1,@Trading_date)
Nodelocation: 448,176,1
Nodesize: 48,24
Defnstate: 2,343,166,416,303,0,MIDM
Valuestate: 2,88,98,596,302,1,MIDM
Reformdef: [Trading_date,Wt_type]
Decision Wt_type
Title: wt type
Definition: Choice(Self,2)
Nodelocation: 448,232,1
Nodesize: 48,24
Domain: ['Equal','More recent']
{!40000|Att_previndexvalue: ['Equal','More recent']}
Close Statistical_function
Module Statistical_functio1
Title: Statistical function applied to uncertainty
Defaultsize: 48,24
Nodelocation: 272,97,1
Nodesize: 64,44
Diagstate: 1,458,239,545,300,17
Alias Simulated_prices1
Title: Simulated prices
Definition: 1
Nodelocation: 208,48,1
Nodesize: 48,24
Original: Simulated_prices
Variable Eoyp
Title: End of year price
Definition: Simulated_prices[Future_date=MakeDate(2008,12,31)]
Nodelocation: 320,48,1
Nodesize: 48,24
Valuestate: 2,174,21,543,351,1,PDFP
Reformval: [Undefined,Undefined,Undefined,Undefined,1,1]
{!40000|Att_resultslicestate: [Stock,4,Sys_localindex('STEP'),1]}
Alias Future_date1
Title: Future date
Definition: 1
Nodelocation: 96,48,1
Nodesize: 48,24
Original: Future_date
Variable Mean1
Title: mean
Definition: Mean(eoyp)
Nodelocation: 208,120,1
Nodesize: 48,24
Valuestate: 2,58,5,416,303,0,MIDM
Variable Sd_eoyp
Title: Sd eoyp
Definition: SDeviation(eoyp)
Nodelocation: 320,120,1
Nodesize: 48,24
Valuestate: 2,30,26,416,303,0,MIDM
Variable Average_
Title: average (vs. mean)
Definition: Average( Sample(Eoyp), Run )
Nodelocation: 432,120,1
Nodesize: 48,24
Valuestate: 2,483,7,416,303,0,SMPL
Variable Min_eoyp
Title: min eoyp
Definition: Stat_min(Eoyp)
Nodelocation: 88,192,1
Nodesize: 48,24
Valuestate: 2,418,20,416,303,0,MIDM
Function Stat_min( x : ContextSamp[I] ; I : Index = Run)
Title: Stat min
Definition: Min(x,I)
Nodelocation: 328,184,1
Nodesize: 48,24
Paramnames: x,I
Function Median( x : ContextSamp [ I ] ; I : Index = Run)
Title: Median
Definition: GetFract( x, 50%, I )
Nodelocation: 440,184,1
Nodesize: 48,24
Paramnames: x,I
Variable Median_eoyp
Title: median eoyp
Definition: Median(eoyp)
Nodelocation: 200,192,1
Nodesize: 48,24
Valuestate: 2,260,242,416,303,0,MIDM
Function Stat_mode(x : ContextSamp [ I ] ; I : Index= Run)
Title: Stat Mode
Definition: var histo := pdf(x,I);~
var bin := histo[DensityIndex='X'];~
var dens := histo[DensityIndex='Y'];~
bin[ .Step = ArgMax( dens, dens.Step )]
Nodelocation: 328,240,1
Nodesize: 48,24
Windstate: 2,514,7,476,224
Paramnames: x,I
Variable Mode_eoyp
Title: Mode eoyp
Definition: Stat_mode(Eoyp)
Nodelocation: 96,248,1
Nodesize: 48,24
Valuestate: 2,24,300,416,303,0,MIDM
Close Statistical_functio1
Module Discrete_vs__continu
Title: Discrete vs. continuous
Defaultsize: 48,24
Nodelocation: 96,208,1
Nodesize: 48,32
Diagstate: 1,70,55,550,300,17
Variable Num_that_increased
Title: Num that increased
Definition: sum( Daily_change>0, stock )
Nodelocation: 96,56,1
Nodesize: 48,24
Windstate: 2,119,84,476,224
Valuestate: 2,504,34,416,410,0,MIDM
Domain: Domcontinuous
Variable Histo___increased
Title: histo # increased
Definition: Pdf( Num_that_increased^2, Trading_date )
Nodelocation: 208,56,1
Nodesize: 48,24
Valuestate: 2,455,323,416,303,0,MIDM
Reformval: [Densityindex,Possible_values]
Variable Cum_prob
Title: Cum prob
Definition: cdf(Num_that_increased,trading_date)
Nodelocation: 208,112,1
Nodesize: 48,24
Valuestate: 2,200,210,416,303,1,MIDM
Reformval: [Sys_localindex('STEP'),Densityindex]
{!40000|Att_coordinateindex: Densityindex}
Chance Count
Title: Count
Definition: Poisson(100) / 4
Nodelocation: 96,192,1
Nodesize: 48,24
Valuestate: 2,152,226,790,375,1,PDFP
Domain: Domdiscretenumeric
Close Discrete_vs__continu
Close Intro_to_statistical