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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationTue, 02 Dec 2008 06:20:34 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t1228224282klhowy1hok4uayu.htm/, Retrieved Fri, 17 May 2024 05:03:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27745, Retrieved Fri, 17 May 2024 05:03:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F R     [Law of Averages] [question 3] [2008-12-01 12:27:05] [379d6c32f73e3218fd773d79e4063d07]
F           [Law of Averages] [Q3] [2008-12-02 13:20:34] [f4914427e726625a358be9269a8b7d03] [Current]
Feedback Forum
2008-12-06 11:54:05 [Bert Moons] [reply] 
Uit de tabel moet je de kleinste variantie kiezen. In dit geval wordt die bereikt door 1 maal trendmatig te differentiëren (d=1) . Hoe kleiner de variantie, hoe beter het model.
2008-12-08 14:19:27 [Alexander Hendrickx] [reply] 
Om het beste differentiatie door te voeren, en dus ook het beste model te creëren, zoeken we de naar de kleinste variantie in de variantiereductiematrix. De bijbehorende d en D waarden geven de in te vullen waarden die de beste differentiatie zullen weergeven. Hier is dat d =1 en D = 0. d = 1  we differentiëren op lange termijn.

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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27745&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27745&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)36.8792144288577Range29Trim Var.22.8996980772287
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85110663983903Range4Trim Var.0
V(Y[t],d=3,D=0)5.45161290322581Range8Trim Var.2.51503988551136
V(Y[t],d=0,D=1)12.5225704379439Range18Trim Var.6.29386365018549
V(Y[t],d=1,D=1)2.07400647282007Range4Trim Var.0
V(Y[t],d=2,D=1)3.53812735989139Range8Trim Var.0
V(Y[t],d=3,D=1)10.1074209763994Range16Trim Var.2.50307574009996
V(Y[t],d=0,D=2)29.2947014595312Range34Trim Var.12.3488636363636
V(Y[t],d=1,D=2)6.31045969353764Range8Trim Var.2.67645136969088
V(Y[t],d=2,D=2)10.3763035120115Range16Trim Var.4.35425169251452
V(Y[t],d=3,D=2)29.1439065467445Range32Trim Var.15.2548676561883

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 36.8792144288577 & Range & 29 & Trim Var. & 22.8996980772287 \tabularnewline
V(Y[t],d=1,D=0) & 1.00168207901747 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.85110663983903 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.45161290322581 & Range & 8 & Trim Var. & 2.51503988551136 \tabularnewline
V(Y[t],d=0,D=1) & 12.5225704379439 & Range & 18 & Trim Var. & 6.29386365018549 \tabularnewline
V(Y[t],d=1,D=1) & 2.07400647282007 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.53812735989139 & Range & 8 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=1) & 10.1074209763994 & Range & 16 & Trim Var. & 2.50307574009996 \tabularnewline
V(Y[t],d=0,D=2) & 29.2947014595312 & Range & 34 & Trim Var. & 12.3488636363636 \tabularnewline
V(Y[t],d=1,D=2) & 6.31045969353764 & Range & 8 & Trim Var. & 2.67645136969088 \tabularnewline
V(Y[t],d=2,D=2) & 10.3763035120115 & Range & 16 & Trim Var. & 4.35425169251452 \tabularnewline
V(Y[t],d=3,D=2) & 29.1439065467445 & Range & 32 & Trim Var. & 15.2548676561883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27745&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]36.8792144288577[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]22.8996980772287[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00168207901747[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]NA[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.85110663983903[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]5.45161290322581[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.51503988551136[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.5225704379439[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.29386365018549[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.07400647282007[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3.53812735989139[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.1074209763994[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]2.50307574009996[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]29.2947014595312[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]12.3488636363636[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.31045969353764[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67645136969088[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.3763035120115[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.35425169251452[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]29.1439065467445[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]15.2548676561883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27745&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)36.8792144288577Range29Trim Var.22.8996980772287
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85110663983903Range4Trim Var.0
V(Y[t],d=3,D=0)5.45161290322581Range8Trim Var.2.51503988551136
V(Y[t],d=0,D=1)12.5225704379439Range18Trim Var.6.29386365018549
V(Y[t],d=1,D=1)2.07400647282007Range4Trim Var.0
V(Y[t],d=2,D=1)3.53812735989139Range8Trim Var.0
V(Y[t],d=3,D=1)10.1074209763994Range16Trim Var.2.50307574009996
V(Y[t],d=0,D=2)29.2947014595312Range34Trim Var.12.3488636363636
V(Y[t],d=1,D=2)6.31045969353764Range8Trim Var.2.67645136969088
V(Y[t],d=2,D=2)10.3763035120115Range16Trim Var.4.35425169251452
V(Y[t],d=3,D=2)29.1439065467445Range32Trim Var.15.2548676561883


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ;
R code (references can be found in the software module):
n <- as.numeric(par1)
p <- as.numeric(par2)
heads=rbinom(n-1,1,p)
a=2*(heads)-1
b=diffinv(a,xi=0)
c=1:n
pheads=(diffinv(heads,xi=.5))/c
bitmap(file='test1.png')
op=par(mfrow=c(2,1))
plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
lines(c,b,col='red')
lines(c,rep(0,n),col='black')
plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
lines(c,pheads,col='blue')
lines(c,rep(.5,n),col='black')
par(op)
dev.off()
b
par1 <- as.numeric(12)
x <- as.array(b)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(x,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')