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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 14:28:38 -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/t12280805601mz7ca1vzu27ya3.htm/, Retrieved Sun, 19 May 2024 01:35:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26740, Retrieved Sun, 19 May 2024 01:35:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [] [2008-11-30 21:28:38] [9ba97de59bb4d2edf0cfeac4ca7d2b73] [Current]
F           [Law of Averages] [Q3] [2008-12-01 19:43:51] [5faef9c71125a233e2c8b38f64296883]
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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=26740&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=26740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26740&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)65.2337314629258Range33Trim Var.41.6069594034797
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02816901408451Range4Trim Var.0
V(Y[t],d=3,D=0)6.06445122346985Range8Trim Var.2.71280758194940
V(Y[t],d=0,D=1)12.9862322011647Range18Trim Var.6.65390155045327
V(Y[t],d=1,D=1)2.09861332927726Range4Trim Var.0
V(Y[t],d=2,D=1)4.37936447329345Range8Trim Var.2.14691429397312
V(Y[t],d=3,D=1)13.2231404958678Range16Trim Var.6.75840399002494
V(Y[t],d=0,D=2)23.2038920831491Range30Trim Var.11.9601829432338
V(Y[t],d=1,D=2)6.45567843659782Range8Trim Var.2.72734132496441
V(Y[t],d=2,D=2)13.5305840269043Range16Trim Var.5.85940425531915
V(Y[t],d=3,D=2)41.1101515748737Range32Trim Var.24.2943573517427

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 65.2337314629258 & Range & 33 & Trim Var. & 41.6069594034797 \tabularnewline
V(Y[t],d=1,D=0) & 1.00168207901747 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.02816901408451 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.06445122346985 & Range & 8 & Trim Var. & 2.71280758194940 \tabularnewline
V(Y[t],d=0,D=1) & 12.9862322011647 & Range & 18 & Trim Var. & 6.65390155045327 \tabularnewline
V(Y[t],d=1,D=1) & 2.09861332927726 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.37936447329345 & Range & 8 & Trim Var. & 2.14691429397312 \tabularnewline
V(Y[t],d=3,D=1) & 13.2231404958678 & Range & 16 & Trim Var. & 6.75840399002494 \tabularnewline
V(Y[t],d=0,D=2) & 23.2038920831491 & Range & 30 & Trim Var. & 11.9601829432338 \tabularnewline
V(Y[t],d=1,D=2) & 6.45567843659782 & Range & 8 & Trim Var. & 2.72734132496441 \tabularnewline
V(Y[t],d=2,D=2) & 13.5305840269043 & Range & 16 & Trim Var. & 5.85940425531915 \tabularnewline
V(Y[t],d=3,D=2) & 41.1101515748737 & Range & 32 & Trim Var. & 24.2943573517427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26740&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]65.2337314629258[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]41.6069594034797[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00168207901747[/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]2.02816901408451[/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]6.06445122346985[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.71280758194940[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.9862322011647[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.65390155045327[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09861332927726[/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]4.37936447329345[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.14691429397312[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.2231404958678[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.75840399002494[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.2038920831491[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]11.9601829432338[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.45567843659782[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72734132496441[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.5305840269043[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.85940425531915[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]41.1101515748737[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]24.2943573517427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26740&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)65.2337314629258Range33Trim Var.41.6069594034797
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02816901408451Range4Trim Var.0
V(Y[t],d=3,D=0)6.06445122346985Range8Trim Var.2.71280758194940
V(Y[t],d=0,D=1)12.9862322011647Range18Trim Var.6.65390155045327
V(Y[t],d=1,D=1)2.09861332927726Range4Trim Var.0
V(Y[t],d=2,D=1)4.37936447329345Range8Trim Var.2.14691429397312
V(Y[t],d=3,D=1)13.2231404958678Range16Trim Var.6.75840399002494
V(Y[t],d=0,D=2)23.2038920831491Range30Trim Var.11.9601829432338
V(Y[t],d=1,D=2)6.45567843659782Range8Trim Var.2.72734132496441
V(Y[t],d=2,D=2)13.5305840269043Range16Trim Var.5.85940425531915
V(Y[t],d=3,D=2)41.1101515748737Range32Trim Var.24.2943573517427


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')