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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 computationFri, 28 Nov 2008 08:50:40 -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/Nov/28/t1227887475ghoo39pji7s1kwi.htm/, Retrieved Sun, 19 May 2024 12:06:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26125, Retrieved Sun, 19 May 2024 12:06:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact223

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         [Law of Averages] [Variance Reductio...] [2008-11-28 15:50:40] [8758b22b4a10c08c31202f233362e983] [Current]
Feedback Forum
2008-12-04 16:31:55 [Matthieu Blondeau] [reply] 
Met de VRM kunnen we nagaan hoe we de tijdreeks stationair kunnen maken, dit wil zeggen welke d en D we hiervoor kunnen instellen. Om dit na te gaan moet men in de tabel de kleinste variantie zoeken. De kleinste waarde bedraagt 0.99987927662554. Deze variantie komt overeen met een waarde voor d=1 en D=0. Dit wil zeggen dat men 1 keer moet differentiëren.
Het differentiëren D=0 en d=1 komt overeen met het Random Walk Model Yt = Yt-1 + et.

Post a new message

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=26125&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=26125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26125&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)66.2286012024048Range31Trim Var.47.4148858893045
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06839430155229Range4Trim Var.0
V(Y[t],d=3,D=0)6.2258064516129Range8Trim Var.2.75409836065574
V(Y[t],d=0,D=1)8.8393812906049Range18Trim Var.3.76136541573151
V(Y[t],d=1,D=1)1.95060038363712Range4Trim Var.0
V(Y[t],d=2,D=1)3.99998302999448Range8Trim Var.2.30568351284176
V(Y[t],d=3,D=1)11.8677004345233Range16Trim Var.6.77273732611606
V(Y[t],d=0,D=2)18.0273330384785Range28Trim Var.8.91941787322738
V(Y[t],d=1,D=2)5.83106373528759Range8Trim Var.2.57304240173321
V(Y[t],d=2,D=2)11.8646756050347Range16Trim Var.6.76660897350552
V(Y[t],d=3,D=2)34.805066829111Range32Trim Var.21.7697639629558

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 66.2286012024048 & Range & 31 & Trim Var. & 47.4148858893045 \tabularnewline
V(Y[t],d=1,D=0) & 1.00190742931646 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.06839430155229 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.2258064516129 & Range & 8 & Trim Var. & 2.75409836065574 \tabularnewline
V(Y[t],d=0,D=1) & 8.8393812906049 & Range & 18 & Trim Var. & 3.76136541573151 \tabularnewline
V(Y[t],d=1,D=1) & 1.95060038363712 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.99998302999448 & Range & 8 & Trim Var. & 2.30568351284176 \tabularnewline
V(Y[t],d=3,D=1) & 11.8677004345233 & Range & 16 & Trim Var. & 6.77273732611606 \tabularnewline
V(Y[t],d=0,D=2) & 18.0273330384785 & Range & 28 & Trim Var. & 8.91941787322738 \tabularnewline
V(Y[t],d=1,D=2) & 5.83106373528759 & Range & 8 & Trim Var. & 2.57304240173321 \tabularnewline
V(Y[t],d=2,D=2) & 11.8646756050347 & Range & 16 & Trim Var. & 6.76660897350552 \tabularnewline
V(Y[t],d=3,D=2) & 34.805066829111 & Range & 32 & Trim Var. & 21.7697639629558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26125&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]66.2286012024048[/C][C]Range[/C][C]31[/C][C]Trim Var.[/C][C]47.4148858893045[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00190742931646[/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]2.06839430155229[/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]6.2258064516129[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.75409836065574[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]8.8393812906049[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]3.76136541573151[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95060038363712[/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]3.99998302999448[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.30568351284176[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.8677004345233[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.77273732611606[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]18.0273330384785[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]8.91941787322738[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.83106373528759[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.57304240173321[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.8646756050347[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.76660897350552[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.805066829111[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.7697639629558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26125&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)66.2286012024048Range31Trim Var.47.4148858893045
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06839430155229Range4Trim Var.0
V(Y[t],d=3,D=0)6.2258064516129Range8Trim Var.2.75409836065574
V(Y[t],d=0,D=1)8.8393812906049Range18Trim Var.3.76136541573151
V(Y[t],d=1,D=1)1.95060038363712Range4Trim Var.0
V(Y[t],d=2,D=1)3.99998302999448Range8Trim Var.2.30568351284176
V(Y[t],d=3,D=1)11.8677004345233Range16Trim Var.6.77273732611606
V(Y[t],d=0,D=2)18.0273330384785Range28Trim Var.8.91941787322738
V(Y[t],d=1,D=2)5.83106373528759Range8Trim Var.2.57304240173321
V(Y[t],d=2,D=2)11.8646756050347Range16Trim Var.6.76660897350552
V(Y[t],d=3,D=2)34.805066829111Range32Trim Var.21.7697639629558


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')