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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 computationSun, 30 Nov 2008 11:04:14 -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/30/t122806829271jil5vitq7dwd8.htm/, Retrieved Sun, 19 May 2024 10:44:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26658, Retrieved Sun, 19 May 2024 10:44:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

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] [] [2008-11-30 10:24:27] [a4ee3bef49b119f4bd2e925060c84f5e]
-           [Law of Averages] [Q3] [2008-11-30 18:04:14] [708e5cce6cfef15b7edd0dea71956401] [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=26658&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=26658&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26658&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)148.029194388778Range44Trim Var.109.205432379785
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)6.07256441877069Range8Trim Var.2.60657476139979
V(Y[t],d=0,D=1)12.3406436193490Range16Trim Var.6.18505138964909
V(Y[t],d=1,D=1)1.95046518112911Range4Trim Var.0
V(Y[t],d=2,D=1)3.78555004030376Range8Trim Var.0.959934919666463
V(Y[t],d=3,D=1)11.4544772940274Range16Trim Var.6.96679796107507
V(Y[t],d=0,D=2)28.49590446705Range30Trim Var.12.9659486510009
V(Y[t],d=1,D=2)5.81432822562736Range8Trim Var.2.59662386556680
V(Y[t],d=2,D=2)11.2219694739565Range16Trim Var.6.51843329018649
V(Y[t],d=3,D=2)34.0762532697889Range28Trim Var.21.3858667779832

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 148.029194388778 & Range & 44 & Trim Var. & 109.205432379785 \tabularnewline
V(Y[t],d=1,D=0) & 0.99862375353116 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.00400798364484 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.07256441877069 & Range & 8 & Trim Var. & 2.60657476139979 \tabularnewline
V(Y[t],d=0,D=1) & 12.3406436193490 & Range & 16 & Trim Var. & 6.18505138964909 \tabularnewline
V(Y[t],d=1,D=1) & 1.95046518112911 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.78555004030376 & Range & 8 & Trim Var. & 0.959934919666463 \tabularnewline
V(Y[t],d=3,D=1) & 11.4544772940274 & Range & 16 & Trim Var. & 6.96679796107507 \tabularnewline
V(Y[t],d=0,D=2) & 28.49590446705 & Range & 30 & Trim Var. & 12.9659486510009 \tabularnewline
V(Y[t],d=1,D=2) & 5.81432822562736 & Range & 8 & Trim Var. & 2.59662386556680 \tabularnewline
V(Y[t],d=2,D=2) & 11.2219694739565 & Range & 16 & Trim Var. & 6.51843329018649 \tabularnewline
V(Y[t],d=3,D=2) & 34.0762532697889 & Range & 28 & Trim Var. & 21.3858667779832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26658&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]148.029194388778[/C][C]Range[/C][C]44[/C][C]Trim Var.[/C][C]109.205432379785[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99862375353116[/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]2.00400798364484[/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]6.07256441877069[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.60657476139979[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.3406436193490[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.18505138964909[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95046518112911[/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]3.78555004030376[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.959934919666463[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.4544772940274[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.96679796107507[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28.49590446705[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]12.9659486510009[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.81432822562736[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59662386556680[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.2219694739565[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.51843329018649[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.0762532697889[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.3858667779832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26658&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26658&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)148.029194388778Range44Trim Var.109.205432379785
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)6.07256441877069Range8Trim Var.2.60657476139979
V(Y[t],d=0,D=1)12.3406436193490Range16Trim Var.6.18505138964909
V(Y[t],d=1,D=1)1.95046518112911Range4Trim Var.0
V(Y[t],d=2,D=1)3.78555004030376Range8Trim Var.0.959934919666463
V(Y[t],d=3,D=1)11.4544772940274Range16Trim Var.6.96679796107507
V(Y[t],d=0,D=2)28.49590446705Range30Trim Var.12.9659486510009
V(Y[t],d=1,D=2)5.81432822562736Range8Trim Var.2.59662386556680
V(Y[t],d=2,D=2)11.2219694739565Range16Trim Var.6.51843329018649
V(Y[t],d=3,D=2)34.0762532697889Range28Trim Var.21.3858667779832


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')