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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 computationSat, 29 Nov 2008 05:09:03 -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/29/t12279606201u5giep9yhwqtxu.htm/, Retrieved Sun, 19 May 2024 05:56:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26229, Retrieved Sun, 19 May 2024 05:56:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

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...] [2008-11-29 12:09:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
F           [Law of Averages] [law of averages q3] [2008-12-02 15:44:46] [0e11af0256e6e0eb6a79430f4c23d663]
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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=26229&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=26229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26229&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)246.068472945892Range49Trim Var.211.665198928888
V(Y[t],d=1,D=0)0.99814086003332Range2Trim Var.NA
V(Y[t],d=2,D=0)1.88329979879276Range4Trim Var.0
V(Y[t],d=3,D=0)5.43548387096774Range8Trim Var.2.64920370442128
V(Y[t],d=0,D=1)11.2937018211196Range16Trim Var.4.44236844075155
V(Y[t],d=1,D=1)2.18091785602623Range4Trim Var.0
V(Y[t],d=2,D=1)4.18962284162742Range8Trim Var.2.28349567779288
V(Y[t],d=3,D=1)12.2479338842975Range16Trim Var.6.854722165067
V(Y[t],d=0,D=2)24.7534188412207Range26Trim Var.13.1640961728203
V(Y[t],d=1,D=2)6.62360204308239Range8Trim Var.2.88082595870207
V(Y[t],d=2,D=2)12.9217758985201Range16Trim Var.6.10832789382071
V(Y[t],d=3,D=2)38.1609990325008Range28Trim Var.22.6580596024863

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 246.068472945892 & Range & 49 & Trim Var. & 211.665198928888 \tabularnewline
V(Y[t],d=1,D=0) & 0.99814086003332 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.88329979879276 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.43548387096774 & Range & 8 & Trim Var. & 2.64920370442128 \tabularnewline
V(Y[t],d=0,D=1) & 11.2937018211196 & Range & 16 & Trim Var. & 4.44236844075155 \tabularnewline
V(Y[t],d=1,D=1) & 2.18091785602623 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.18962284162742 & Range & 8 & Trim Var. & 2.28349567779288 \tabularnewline
V(Y[t],d=3,D=1) & 12.2479338842975 & Range & 16 & Trim Var. & 6.854722165067 \tabularnewline
V(Y[t],d=0,D=2) & 24.7534188412207 & Range & 26 & Trim Var. & 13.1640961728203 \tabularnewline
V(Y[t],d=1,D=2) & 6.62360204308239 & Range & 8 & Trim Var. & 2.88082595870207 \tabularnewline
V(Y[t],d=2,D=2) & 12.9217758985201 & Range & 16 & Trim Var. & 6.10832789382071 \tabularnewline
V(Y[t],d=3,D=2) & 38.1609990325008 & Range & 28 & Trim Var. & 22.6580596024863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26229&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]246.068472945892[/C][C]Range[/C][C]49[/C][C]Trim Var.[/C][C]211.665198928888[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99814086003332[/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]1.88329979879276[/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]5.43548387096774[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.64920370442128[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.2937018211196[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.44236844075155[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.18091785602623[/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]4.18962284162742[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.28349567779288[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.2479338842975[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.854722165067[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.7534188412207[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]13.1640961728203[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.62360204308239[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.88082595870207[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.9217758985201[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.10832789382071[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.1609990325008[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]22.6580596024863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26229&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)246.068472945892Range49Trim Var.211.665198928888
V(Y[t],d=1,D=0)0.99814086003332Range2Trim Var.NA
V(Y[t],d=2,D=0)1.88329979879276Range4Trim Var.0
V(Y[t],d=3,D=0)5.43548387096774Range8Trim Var.2.64920370442128
V(Y[t],d=0,D=1)11.2937018211196Range16Trim Var.4.44236844075155
V(Y[t],d=1,D=1)2.18091785602623Range4Trim Var.0
V(Y[t],d=2,D=1)4.18962284162742Range8Trim Var.2.28349567779288
V(Y[t],d=3,D=1)12.2479338842975Range16Trim Var.6.854722165067
V(Y[t],d=0,D=2)24.7534188412207Range26Trim Var.13.1640961728203
V(Y[t],d=1,D=2)6.62360204308239Range8Trim Var.2.88082595870207
V(Y[t],d=2,D=2)12.9217758985201Range16Trim Var.6.10832789382071
V(Y[t],d=3,D=2)38.1609990325008Range28Trim Var.22.6580596024863


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')