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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 11:49:21 -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/t1228157402351thwdhk12l3zr.htm/, Retrieved Sun, 05 May 2024 13:23:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27138, Retrieved Sun, 05 May 2024 13:23:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact254

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] [Random Walk] [2008-11-29 12:49:16] [6743688719638b0cb1c0a6e0bf433315]
-           [Law of Averages] [q4] [2008-12-01 18:49:21] [5d823194959040fa9b19b8c8302177e6] [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'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=27138&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=27138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27138&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)105.006909819639Range40Trim Var.79.4752117289869
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.89939637826962Range4Trim Var.0
V(Y[t],d=3,D=0)5.48387096774194Range8Trim Var.2.6901386508802
V(Y[t],d=0,D=1)11.0791227656781Range18Trim Var.6.50292905185507
V(Y[t],d=1,D=1)2.08215242392746Range4Trim Var.0
V(Y[t],d=2,D=1)3.93400364855119Range8Trim Var.2.19631520532741
V(Y[t],d=3,D=1)11.2561301865894Range16Trim Var.5.9012758886713
V(Y[t],d=0,D=2)20.916125608138Range28Trim Var.11.5137516780834
V(Y[t],d=1,D=2)6.43865867199645Range8Trim Var.2.66779368638951
V(Y[t],d=2,D=2)12.0168954781849Range16Trim Var.6.5963442498096
V(Y[t],d=3,D=2)34.1186440677966Range32Trim Var.19.4724343689861

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 105.006909819639 & Range & 40 & Trim Var. & 79.4752117289869 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & 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) & 5.48387096774194 & Range & 8 & Trim Var. & 2.6901386508802 \tabularnewline
V(Y[t],d=0,D=1) & 11.0791227656781 & Range & 18 & Trim Var. & 6.50292905185507 \tabularnewline
V(Y[t],d=1,D=1) & 2.08215242392746 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.93400364855119 & Range & 8 & Trim Var. & 2.19631520532741 \tabularnewline
V(Y[t],d=3,D=1) & 11.2561301865894 & Range & 16 & Trim Var. & 5.9012758886713 \tabularnewline
V(Y[t],d=0,D=2) & 20.916125608138 & Range & 28 & Trim Var. & 11.5137516780834 \tabularnewline
V(Y[t],d=1,D=2) & 6.43865867199645 & Range & 8 & Trim Var. & 2.66779368638951 \tabularnewline
V(Y[t],d=2,D=2) & 12.0168954781849 & Range & 16 & Trim Var. & 6.5963442498096 \tabularnewline
V(Y[t],d=3,D=2) & 34.1186440677966 & Range & 32 & Trim Var. & 19.4724343689861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27138&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]105.006909819639[/C][C]Range[/C][C]40[/C][C]Trim Var.[/C][C]79.4752117289869[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00132795711906[/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]5.48387096774194[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.6901386508802[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.0791227656781[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.50292905185507[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.08215242392746[/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]3.93400364855119[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.19631520532741[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.2561301865894[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.9012758886713[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.916125608138[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]11.5137516780834[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.43865867199645[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66779368638951[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.0168954781849[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.5963442498096[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.1186440677966[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]19.4724343689861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27138&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)105.006909819639Range40Trim Var.79.4752117289869
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.89939637826962Range4Trim Var.0
V(Y[t],d=3,D=0)5.48387096774194Range8Trim Var.2.6901386508802
V(Y[t],d=0,D=1)11.0791227656781Range18Trim Var.6.50292905185507
V(Y[t],d=1,D=1)2.08215242392746Range4Trim Var.0
V(Y[t],d=2,D=1)3.93400364855119Range8Trim Var.2.19631520532741
V(Y[t],d=3,D=1)11.2561301865894Range16Trim Var.5.9012758886713
V(Y[t],d=0,D=2)20.916125608138Range28Trim Var.11.5137516780834
V(Y[t],d=1,D=2)6.43865867199645Range8Trim Var.2.66779368638951
V(Y[t],d=2,D=2)12.0168954781849Range16Trim Var.6.5963442498096
V(Y[t],d=3,D=2)34.1186440677966Range32Trim Var.19.4724343689861


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')