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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 computationMon, 01 Dec 2008 12:43:51 -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/01/t1228160681nyqf2f48r8lzosu.htm/, Retrieved Sun, 05 May 2024 15:14:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27259, Retrieved Sun, 05 May 2024 15:14:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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]
-       [Law of Averages] [] [2008-11-30 21:28:38] [8b0d202c3a0c4ea223fd8b8e731dacd8]
F           [Law of Averages] [Q3] [2008-12-01 19:43:51] [2fdb1a8e4a6fa49ce74bdce2c154874d] [Current]
Feedback Forum
2008-12-08 10:17:42 [Joris Deboel] [reply] 
Gebruikte methode: Random-Walk Simulation

In dit model vinden we een tabel terug. In de eerste kolom staat symbolisch wat in de rij wordt weergegeven.
De d en D uit die bepaalde formule bepaalt hoeveel keer de formule gedifferentieerd wordt.
Deze formule wordt gebruikt om de tijdreeks stationair te maken. Dat betekent dat er geen trend mag inzitten en dat er geen ongelijke spreiding mag voorkomen.
In de tweede kolom van de tabel vind je de variantie van de tijdreeks. Indien d=0 en D=0 dan wordt de formule niet gedifferentieerd.
De bedoeling is dat je die waarde pakt waar de variantie het kleinste is. Dit is het geval in rij 2. Daar waar je 1 keer hebt gedifferentieerd

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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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27259&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27259&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)45.5907815631262Range28Trim Var.34.3598622903293
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)1.89939637826962Range4Trim Var.0
V(Y[t],d=3,D=0)5.39514506393198Range8Trim Var.2.75060440742757
V(Y[t],d=0,D=1)8.99828323290807Range18Trim Var.4.13389132147609
V(Y[t],d=1,D=1)1.9917019460711Range4Trim Var.0
V(Y[t],d=2,D=1)3.82673624368928Range8Trim Var.2.26838612205255
V(Y[t],d=3,D=1)10.7768595041322Range16Trim Var.6.33331071145798
V(Y[t],d=0,D=2)19.1813887660327Range22Trim Var.9.96009483470524
V(Y[t],d=1,D=2)5.74681767710415Range8Trim Var.2.8285358529261
V(Y[t],d=2,D=2)11.1289640591966Range16Trim Var.6.74139025364959
V(Y[t],d=3,D=2)31.4745046045795Range30Trim Var.17.5301163943838

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 45.5907815631262 & Range & 28 & Trim Var. & 34.3598622903293 \tabularnewline
V(Y[t],d=1,D=0) & 1.00110260682007 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.89939637826962 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.39514506393198 & Range & 8 & Trim Var. & 2.75060440742757 \tabularnewline
V(Y[t],d=0,D=1) & 8.99828323290807 & Range & 18 & Trim Var. & 4.13389132147609 \tabularnewline
V(Y[t],d=1,D=1) & 1.9917019460711 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.82673624368928 & Range & 8 & Trim Var. & 2.26838612205255 \tabularnewline
V(Y[t],d=3,D=1) & 10.7768595041322 & Range & 16 & Trim Var. & 6.33331071145798 \tabularnewline
V(Y[t],d=0,D=2) & 19.1813887660327 & Range & 22 & Trim Var. & 9.96009483470524 \tabularnewline
V(Y[t],d=1,D=2) & 5.74681767710415 & Range & 8 & Trim Var. & 2.8285358529261 \tabularnewline
V(Y[t],d=2,D=2) & 11.1289640591966 & Range & 16 & Trim Var. & 6.74139025364959 \tabularnewline
V(Y[t],d=3,D=2) & 31.4745046045795 & Range & 30 & Trim Var. & 17.5301163943838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27259&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]45.5907815631262[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]34.3598622903293[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00110260682007[/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]1.89939637826962[/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]5.39514506393198[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.75060440742757[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]8.99828323290807[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.13389132147609[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.9917019460711[/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]3.82673624368928[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.26838612205255[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.7768595041322[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.33331071145798[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.1813887660327[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]9.96009483470524[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.74681767710415[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.8285358529261[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.1289640591966[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.74139025364959[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]31.4745046045795[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]17.5301163943838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27259&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)45.5907815631262Range28Trim Var.34.3598622903293
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)1.89939637826962Range4Trim Var.0
V(Y[t],d=3,D=0)5.39514506393198Range8Trim Var.2.75060440742757
V(Y[t],d=0,D=1)8.99828323290807Range18Trim Var.4.13389132147609
V(Y[t],d=1,D=1)1.9917019460711Range4Trim Var.0
V(Y[t],d=2,D=1)3.82673624368928Range8Trim Var.2.26838612205255
V(Y[t],d=3,D=1)10.7768595041322Range16Trim Var.6.33331071145798
V(Y[t],d=0,D=2)19.1813887660327Range22Trim Var.9.96009483470524
V(Y[t],d=1,D=2)5.74681767710415Range8Trim Var.2.8285358529261
V(Y[t],d=2,D=2)11.1289640591966Range16Trim Var.6.74139025364959
V(Y[t],d=3,D=2)31.4745046045795Range30Trim Var.17.5301163943838


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')