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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 06:11:05 -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/t12278779038aioh7gp2m9p8ug.htm/, Retrieved Sun, 19 May 2024 10:04:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26075, Retrieved Sun, 19 May 2024 10:04:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181

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] [Non stationary ti...] [2008-11-28 13:11:05] [0f30549460cf4ec26d9cf94b1fcf7789] [Current]
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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=26075&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=26075&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26075&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)96.9489218436874Range35Trim Var.78.4214131218457
V(Y[t],d=1,D=0)0.99949296182727Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.91127409619004Range8Trim Var.2.69123539703144
V(Y[t],d=0,D=1)9.76463459790622Range14Trim Var.4.24348967233060
V(Y[t],d=1,D=1)2.01630880252829Range4Trim Var.0
V(Y[t],d=2,D=1)3.76082474226804Range8Trim Var.2.25917372337696
V(Y[t],d=3,D=1)10.9999829598705Range16Trim Var.6.65976967500084
V(Y[t],d=0,D=2)24.2293321539142Range24Trim Var.11.7203601090144
V(Y[t],d=1,D=2)5.9829624694648Range8Trim Var.2.73366427537698
V(Y[t],d=2,D=2)10.968269685373Range16Trim Var.6.64245387346487
V(Y[t],d=3,D=2)32.2118464901279Range28Trim Var.20.9745390290638

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 96.9489218436874 & Range & 35 & Trim Var. & 78.4214131218457 \tabularnewline
V(Y[t],d=1,D=0) & 0.99949296182727 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.98791140416798 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.91127409619004 & Range & 8 & Trim Var. & 2.69123539703144 \tabularnewline
V(Y[t],d=0,D=1) & 9.76463459790622 & Range & 14 & Trim Var. & 4.24348967233060 \tabularnewline
V(Y[t],d=1,D=1) & 2.01630880252829 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.76082474226804 & Range & 8 & Trim Var. & 2.25917372337696 \tabularnewline
V(Y[t],d=3,D=1) & 10.9999829598705 & Range & 16 & Trim Var. & 6.65976967500084 \tabularnewline
V(Y[t],d=0,D=2) & 24.2293321539142 & Range & 24 & Trim Var. & 11.7203601090144 \tabularnewline
V(Y[t],d=1,D=2) & 5.9829624694648 & Range & 8 & Trim Var. & 2.73366427537698 \tabularnewline
V(Y[t],d=2,D=2) & 10.968269685373 & Range & 16 & Trim Var. & 6.64245387346487 \tabularnewline
V(Y[t],d=3,D=2) & 32.2118464901279 & Range & 28 & Trim Var. & 20.9745390290638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26075&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]96.9489218436874[/C][C]Range[/C][C]35[/C][C]Trim Var.[/C][C]78.4214131218457[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99949296182727[/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]1.98791140416798[/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]5.91127409619004[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69123539703144[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9.76463459790622[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]4.24348967233060[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.01630880252829[/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]3.76082474226804[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.25917372337696[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.9999829598705[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.65976967500084[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.2293321539142[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]11.7203601090144[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.9829624694648[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.73366427537698[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.968269685373[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.64245387346487[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]32.2118464901279[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]20.9745390290638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26075&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26075&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)96.9489218436874Range35Trim Var.78.4214131218457
V(Y[t],d=1,D=0)0.99949296182727Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.91127409619004Range8Trim Var.2.69123539703144
V(Y[t],d=0,D=1)9.76463459790622Range14Trim Var.4.24348967233060
V(Y[t],d=1,D=1)2.01630880252829Range4Trim Var.0
V(Y[t],d=2,D=1)3.76082474226804Range8Trim Var.2.25917372337696
V(Y[t],d=3,D=1)10.9999829598705Range16Trim Var.6.65976967500084
V(Y[t],d=0,D=2)24.2293321539142Range24Trim Var.11.7203601090144
V(Y[t],d=1,D=2)5.9829624694648Range8Trim Var.2.73366427537698
V(Y[t],d=2,D=2)10.968269685373Range16Trim Var.6.64245387346487
V(Y[t],d=3,D=2)32.2118464901279Range28Trim Var.20.9745390290638


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')