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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationMon, 01 Dec 2008 08:26:29 -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/t1228145211qj06yeqmsvc3y7p.htm/, Retrieved Sun, 05 May 2024 16:46:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26945, Retrieved Sun, 05 May 2024 16:46:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

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] [Q3] [2008-12-01 15:26:29] [ee28d11f695cd3bc1f8bbd77ba77987a] [Current]
Feedback Forum
2008-12-08 19:43:03 [8e2cc0b2ef568da46d009b2f601285b2] [reply] 
Correcte berekening, conclusie/antwoord ontbreken enkel een blog link. We vinden de laagste waarde bij d=1 en D=0. Kleinste waarde zoeken, 1 is de kleinst mogelijke waarde deze is het best benaderd in V(Y[t],d=1,D=0).

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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=26945&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=26945&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26945&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)53.4210981963928Range29Trim Var.37.7820187564374
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93962166573740Range4Trim Var.0
V(Y[t],d=3,D=0)5.89514506393198Range8Trim Var.2.47523403761992
V(Y[t],d=0,D=1)14.3927693809540Range22Trim Var.6.4714550194582
V(Y[t],d=1,D=1)2.09874853178526Range4Trim Var.0
V(Y[t],d=2,D=1)4.22268041237113Range8Trim Var.2.30215827338129
V(Y[t],d=3,D=1)13.0165118854903Range16Trim Var.6.05965430829532
V(Y[t],d=0,D=2)29.5399911543565Range28Trim Var.16.5871326525720
V(Y[t],d=1,D=2)6.50631134799023Range8Trim Var.2.67630168787419
V(Y[t],d=2,D=2)13.1584910036485Range16Trim Var.6.35040945591392
V(Y[t],d=3,D=2)40.864406779661Range32Trim Var.23.6754507628294

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 53.4210981963928 & Range & 29 & Trim Var. & 37.7820187564374 \tabularnewline
V(Y[t],d=1,D=0) & 1.00023339852396 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.93962166573740 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.89514506393198 & Range & 8 & Trim Var. & 2.47523403761992 \tabularnewline
V(Y[t],d=0,D=1) & 14.3927693809540 & Range & 22 & Trim Var. & 6.4714550194582 \tabularnewline
V(Y[t],d=1,D=1) & 2.09874853178526 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.22268041237113 & Range & 8 & Trim Var. & 2.30215827338129 \tabularnewline
V(Y[t],d=3,D=1) & 13.0165118854903 & Range & 16 & Trim Var. & 6.05965430829532 \tabularnewline
V(Y[t],d=0,D=2) & 29.5399911543565 & Range & 28 & Trim Var. & 16.5871326525720 \tabularnewline
V(Y[t],d=1,D=2) & 6.50631134799023 & Range & 8 & Trim Var. & 2.67630168787419 \tabularnewline
V(Y[t],d=2,D=2) & 13.1584910036485 & Range & 16 & Trim Var. & 6.35040945591392 \tabularnewline
V(Y[t],d=3,D=2) & 40.864406779661 & Range & 32 & Trim Var. & 23.6754507628294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26945&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]53.4210981963928[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]37.7820187564374[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00023339852396[/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]1.93962166573740[/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]5.89514506393198[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.47523403761992[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.3927693809540[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]6.4714550194582[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09874853178526[/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]4.22268041237113[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.30215827338129[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.0165118854903[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.05965430829532[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]29.5399911543565[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]16.5871326525720[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.50631134799023[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67630168787419[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.1584910036485[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.35040945591392[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]40.864406779661[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]23.6754507628294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26945&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26945&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)53.4210981963928Range29Trim Var.37.7820187564374
V(Y[t],d=1,D=0)1.00023339852396Range2Trim Var.NA
V(Y[t],d=2,D=0)1.93962166573740Range4Trim Var.0
V(Y[t],d=3,D=0)5.89514506393198Range8Trim Var.2.47523403761992
V(Y[t],d=0,D=1)14.3927693809540Range22Trim Var.6.4714550194582
V(Y[t],d=1,D=1)2.09874853178526Range4Trim Var.0
V(Y[t],d=2,D=1)4.22268041237113Range8Trim Var.2.30215827338129
V(Y[t],d=3,D=1)13.0165118854903Range16Trim Var.6.05965430829532
V(Y[t],d=0,D=2)29.5399911543565Range28Trim Var.16.5871326525720
V(Y[t],d=1,D=2)6.50631134799023Range8Trim Var.2.67630168787419
V(Y[t],d=2,D=2)13.1584910036485Range16Trim Var.6.35040945591392
V(Y[t],d=3,D=2)40.864406779661Range32Trim Var.23.6754507628294


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')