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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 computationTue, 02 Dec 2008 13:17:35 -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/02/t1228249103xguvpmp63ri7yyv.htm/, Retrieved Sat, 18 May 2024 05:52:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28355, Retrieved Sat, 18 May 2024 05:52:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

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...] [2008-12-02 20:15:47] [1a689e9ccc515e1757f0522229a687e9]
-           [Law of Averages] [Non stationary ti...] [2008-12-02 20:17:35] [74a138e5b32af267311b5ad4cd13bf7e] [Current]
-             [Law of Averages] [Non stationary ti...] [2008-12-02 20:18:57] [1a689e9ccc515e1757f0522229a687e9]
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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 time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28355&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]0 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=28355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28355&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)25.9708857715431Range25Trim Var.15.2174839185912
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.79837087038359Range8Trim Var.2.68351982318000
V(Y[t],d=0,D=1)12.0240347392870Range20Trim Var.6.6758268590455
V(Y[t],d=1,D=1)2.05700475743825Range4Trim Var.0
V(Y[t],d=2,D=1)3.89278350515464Range8Trim Var.0.967475950526798
V(Y[t],d=3,D=1)11.4214876033058Range16Trim Var.6.52138554216867
V(Y[t],d=0,D=2)28.3763113666519Range30Trim Var.15.1086784650003
V(Y[t],d=1,D=2)6.22777703753053Range8Trim Var.2.76245828245828
V(Y[t],d=2,D=2)11.5348837209302Range16Trim Var.6.88470391794382
V(Y[t],d=3,D=2)33.4915254237288Range32Trim Var.21.8033343660000

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 25.9708857715431 & Range & 25 & Trim Var. & 15.2174839185912 \tabularnewline
V(Y[t],d=1,D=0) & 1.00200400801603 & 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) & 5.79837087038359 & Range & 8 & Trim Var. & 2.68351982318000 \tabularnewline
V(Y[t],d=0,D=1) & 12.0240347392870 & Range & 20 & Trim Var. & 6.6758268590455 \tabularnewline
V(Y[t],d=1,D=1) & 2.05700475743825 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.89278350515464 & Range & 8 & Trim Var. & 0.967475950526798 \tabularnewline
V(Y[t],d=3,D=1) & 11.4214876033058 & Range & 16 & Trim Var. & 6.52138554216867 \tabularnewline
V(Y[t],d=0,D=2) & 28.3763113666519 & Range & 30 & Trim Var. & 15.1086784650003 \tabularnewline
V(Y[t],d=1,D=2) & 6.22777703753053 & Range & 8 & Trim Var. & 2.76245828245828 \tabularnewline
V(Y[t],d=2,D=2) & 11.5348837209302 & Range & 16 & Trim Var. & 6.88470391794382 \tabularnewline
V(Y[t],d=3,D=2) & 33.4915254237288 & Range & 32 & Trim Var. & 21.8033343660000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28355&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]25.9708857715431[/C][C]Range[/C][C]25[/C][C]Trim Var.[/C][C]15.2174839185912[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00200400801603[/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]5.79837087038359[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.68351982318000[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.0240347392870[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.6758268590455[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.05700475743825[/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]3.89278350515464[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.967475950526798[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.4214876033058[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.52138554216867[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28.3763113666519[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]15.1086784650003[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.22777703753053[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.76245828245828[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.5348837209302[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.88470391794382[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]33.4915254237288[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.8033343660000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28355&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)25.9708857715431Range25Trim Var.15.2174839185912
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.79837087038359Range8Trim Var.2.68351982318000
V(Y[t],d=0,D=1)12.0240347392870Range20Trim Var.6.6758268590455
V(Y[t],d=1,D=1)2.05700475743825Range4Trim Var.0
V(Y[t],d=2,D=1)3.89278350515464Range8Trim Var.0.967475950526798
V(Y[t],d=3,D=1)11.4214876033058Range16Trim Var.6.52138554216867
V(Y[t],d=0,D=2)28.3763113666519Range30Trim Var.15.1086784650003
V(Y[t],d=1,D=2)6.22777703753053Range8Trim Var.2.76245828245828
V(Y[t],d=2,D=2)11.5348837209302Range16Trim Var.6.88470391794382
V(Y[t],d=3,D=2)33.4915254237288Range32Trim Var.21.8033343660000


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')