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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 06:08:16 -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/t1227877749wrahewhlzkg7gxl.htm/, Retrieved Sun, 19 May 2024 09:24:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26071, Retrieved Sun, 19 May 2024 09:24:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

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] [q3] [2008-11-28 13:08:16] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
Feedback Forum
2008-12-06 15:20:04 [Wim Golsteyn] [reply] 
De variantie van de reeks is het kleinst bij V(Y[t],d=1,D=0). In de 2de kolom van de tabel zien we hier immers het laagste getal. Dit wil zeggen dat indien we de reeks 1x differentiëren we het lange termijn effect kunnen uitzuiveren, en zo een meer stabiel gemiddelde krijgen van de reeks.
2008-12-07 14:42:28 [Chi-Kwong Man] [reply] 
In de eerste kolom van de variance reduction matrix vindt je de wijze van variantie. De kleine 'd' staat voor differentiëren (lange termijn effect zuiveren,
waardoor men een stabieler gemiddelde krijgt). V(Y[t],d=1,D=0) betekent dat men '1x' differentiërt, wat de kleinste variantie weergeeft in de tweede kolom (de kleinste kan men vinden in de tweede rij (1.00190742931646)).
2008-12-08 17:14:05 [Lindsay Heyndrickx] [reply] 
Dit is correct.

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=26071&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=26071&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26071&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)64.5179799599198Range32Trim Var.44.596415681135
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)5.9757902252223Range8Trim Var.2.65759630686298
V(Y[t],d=0,D=1)12.4124112162117Range18Trim Var.6.9656015365811
V(Y[t],d=1,D=1)1.82709289257316Range4Trim Var.0
V(Y[t],d=2,D=1)3.64529294472021Range8Trim Var.0.901687888658573
V(Y[t],d=3,D=1)10.8842804805317Range16Trim Var.5.93859118153225
V(Y[t],d=0,D=2)21.498929677134Range28Trim Var.9.86750352314839
V(Y[t],d=1,D=2)5.18115034421497Range8Trim Var.2.57416647300863
V(Y[t],d=2,D=2)10.3340380549683Range16Trim Var.6.01801966404403
V(Y[t],d=3,D=2)30.8724334396388Range28Trim Var.16.550574133633

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 64.5179799599198 & Range & 32 & Trim Var. & 44.596415681135 \tabularnewline
V(Y[t],d=1,D=0) & 1.00190742931646 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.99597585513078 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.9757902252223 & Range & 8 & Trim Var. & 2.65759630686298 \tabularnewline
V(Y[t],d=0,D=1) & 12.4124112162117 & Range & 18 & Trim Var. & 6.9656015365811 \tabularnewline
V(Y[t],d=1,D=1) & 1.82709289257316 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.64529294472021 & Range & 8 & Trim Var. & 0.901687888658573 \tabularnewline
V(Y[t],d=3,D=1) & 10.8842804805317 & Range & 16 & Trim Var. & 5.93859118153225 \tabularnewline
V(Y[t],d=0,D=2) & 21.498929677134 & Range & 28 & Trim Var. & 9.86750352314839 \tabularnewline
V(Y[t],d=1,D=2) & 5.18115034421497 & Range & 8 & Trim Var. & 2.57416647300863 \tabularnewline
V(Y[t],d=2,D=2) & 10.3340380549683 & Range & 16 & Trim Var. & 6.01801966404403 \tabularnewline
V(Y[t],d=3,D=2) & 30.8724334396388 & Range & 28 & Trim Var. & 16.550574133633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26071&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]64.5179799599198[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]44.596415681135[/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]1.99597585513078[/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]5.9757902252223[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.65759630686298[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.4124112162117[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.9656015365811[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.82709289257316[/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]3.64529294472021[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.901687888658573[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.8842804805317[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.93859118153225[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.498929677134[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]9.86750352314839[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.18115034421497[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.57416647300863[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.3340380549683[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.01801966404403[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]30.8724334396388[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]16.550574133633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26071&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26071&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)64.5179799599198Range32Trim Var.44.596415681135
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)5.9757902252223Range8Trim Var.2.65759630686298
V(Y[t],d=0,D=1)12.4124112162117Range18Trim Var.6.9656015365811
V(Y[t],d=1,D=1)1.82709289257316Range4Trim Var.0
V(Y[t],d=2,D=1)3.64529294472021Range8Trim Var.0.901687888658573
V(Y[t],d=3,D=1)10.8842804805317Range16Trim Var.5.93859118153225
V(Y[t],d=0,D=2)21.498929677134Range28Trim Var.9.86750352314839
V(Y[t],d=1,D=2)5.18115034421497Range8Trim Var.2.57416647300863
V(Y[t],d=2,D=2)10.3340380549683Range16Trim Var.6.01801966404403
V(Y[t],d=3,D=2)30.8724334396388Range28Trim Var.16.550574133633


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')