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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 computationWed, 03 Dec 2008 12:41:57 -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/03/t12283334019j1ql8mofy6vqmy.htm/, Retrieved Tue, 21 May 2024 06:29:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28864, Retrieved Tue, 21 May 2024 06:29:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact222

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] [q3] [2008-12-01 10:35:08] [5161246d1ccc1b670cc664d03050f084]
-           [Law of Averages] [Q3] [2008-12-03 19:41:57] [787873b6436f665b5b192a0bdb2e43c9] [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=28864&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=28864&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28864&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)128.097378757515Range43Trim Var.94.6289334323187
V(Y[t],d=1,D=0)0.997078494338074Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.95966119296424Range8Trim Var.2.53981204924601
V(Y[t],d=0,D=1)12.1906453024540Range16Trim Var.6.13070571740146
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.31658805290761
V(Y[t],d=3,D=1)12.2314049586777Range16Trim Var.6.24563591022444
V(Y[t],d=0,D=2)25.1029986731535Range24Trim Var.13.0497417499936
V(Y[t],d=1,D=2)5.90688874083944Range8Trim Var.2.70323176361958
V(Y[t],d=2,D=2)12.0591252531200Range16Trim Var.6.5
V(Y[t],d=3,D=2)37.1948973375856Range32Trim Var.21.1471321695761

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 128.097378757515 & Range & 43 & Trim Var. & 94.6289334323187 \tabularnewline
V(Y[t],d=1,D=0) & 0.997078494338074 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.96378269617706 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.95966119296424 & Range & 8 & Trim Var. & 2.53981204924601 \tabularnewline
V(Y[t],d=0,D=1) & 12.1906453024540 & Range & 16 & Trim Var. & 6.13070571740146 \tabularnewline
V(Y[t],d=1,D=1) & 1.98352219433670 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.98348818463366 & Range & 8 & Trim Var. & 2.31658805290761 \tabularnewline
V(Y[t],d=3,D=1) & 12.2314049586777 & Range & 16 & Trim Var. & 6.24563591022444 \tabularnewline
V(Y[t],d=0,D=2) & 25.1029986731535 & Range & 24 & Trim Var. & 13.0497417499936 \tabularnewline
V(Y[t],d=1,D=2) & 5.90688874083944 & Range & 8 & Trim Var. & 2.70323176361958 \tabularnewline
V(Y[t],d=2,D=2) & 12.0591252531200 & Range & 16 & Trim Var. & 6.5 \tabularnewline
V(Y[t],d=3,D=2) & 37.1948973375856 & Range & 32 & Trim Var. & 21.1471321695761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28864&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]128.097378757515[/C][C]Range[/C][C]43[/C][C]Trim Var.[/C][C]94.6289334323187[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.997078494338074[/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]1.96378269617706[/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]5.95966119296424[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.53981204924601[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.1906453024540[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.13070571740146[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.98352219433670[/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]3.98348818463366[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.31658805290761[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.2314049586777[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.24563591022444[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.1029986731535[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]13.0497417499936[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.90688874083944[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.70323176361958[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.0591252531200[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.5[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.1948973375856[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.1471321695761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28864&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28864&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)128.097378757515Range43Trim Var.94.6289334323187
V(Y[t],d=1,D=0)0.997078494338074Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.95966119296424Range8Trim Var.2.53981204924601
V(Y[t],d=0,D=1)12.1906453024540Range16Trim Var.6.13070571740146
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.31658805290761
V(Y[t],d=3,D=1)12.2314049586777Range16Trim Var.6.24563591022444
V(Y[t],d=0,D=2)25.1029986731535Range24Trim Var.13.0497417499936
V(Y[t],d=1,D=2)5.90688874083944Range8Trim Var.2.70323176361958
V(Y[t],d=2,D=2)12.0591252531200Range16Trim Var.6.5
V(Y[t],d=3,D=2)37.1948973375856Range32Trim Var.21.1471321695761


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')