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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 computationMon, 01 Dec 2008 05:27:05 -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/01/t1228134450b6d8aw8gnguvz98.htm/, Retrieved Sun, 05 May 2024 15:04:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26896, Retrieved Sun, 05 May 2024 15:04:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact203

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 R       [Law of Averages] [question 3] [2008-12-01 12:27:05] [490fee4f334e2e025c95681783e3fd0b] [Current]
F           [Law of Averages] [Q3] [2008-12-02 13:20:34] [d811f621c525a990f9b60f1ae1e2e8fd]
F           [Law of Averages] [variance reductio...] [2008-12-02 13:30:16] [98f6eecc397b06503dbf024e1e936f30]
Feedback Forum
2008-12-08 15:49:54 [Alexander Hendrickx] [reply] 
D en d waarden die de beste differentiatie tot gevolg hebben kunnen we vinden aan de hand van een variantie reductiematricx. De d en D waarden met de kleinste variantie geven de optimale differentiatie waar. Hier is dat D = 0 en d = 1. d= 1 betekent dat we op lange termijn differentiëren, niet op seizoenaliteit.

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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=26896&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=26896&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26896&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)41.0553266533066Range28Trim Var.28.7095723988725
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.85483870967742Range8Trim Var.2.68381008222697
V(Y[t],d=0,D=1)14.0030969131854Range18Trim Var.7.01043411372067
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)4.18969072164948Range8Trim Var.2.42573358878693
V(Y[t],d=3,D=1)12.7768595041322Range16Trim Var.6.80059738883268
V(Y[t],d=0,D=2)26.9293940734188Range28Trim Var.13.8412748376943
V(Y[t],d=1,D=2)6.31223628691983Range8Trim Var.2.64900572969329
V(Y[t],d=2,D=2)12.8116787539808Range16Trim Var.6.78296750379013
V(Y[t],d=3,D=2)39.2965922528398Range32Trim Var.21.1640894484884

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 41.0553266533066 & Range & 28 & Trim Var. & 28.7095723988725 \tabularnewline
V(Y[t],d=1,D=0) & 1.00181085061690 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.97181482469112 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.85483870967742 & Range & 8 & Trim Var. & 2.68381008222697 \tabularnewline
V(Y[t],d=0,D=1) & 14.0030969131854 & Range & 18 & Trim Var. & 7.01043411372067 \tabularnewline
V(Y[t],d=1,D=1) & 2.06582672108568 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.18969072164948 & Range & 8 & Trim Var. & 2.42573358878693 \tabularnewline
V(Y[t],d=3,D=1) & 12.7768595041322 & Range & 16 & Trim Var. & 6.80059738883268 \tabularnewline
V(Y[t],d=0,D=2) & 26.9293940734188 & Range & 28 & Trim Var. & 13.8412748376943 \tabularnewline
V(Y[t],d=1,D=2) & 6.31223628691983 & Range & 8 & Trim Var. & 2.64900572969329 \tabularnewline
V(Y[t],d=2,D=2) & 12.8116787539808 & Range & 16 & Trim Var. & 6.78296750379013 \tabularnewline
V(Y[t],d=3,D=2) & 39.2965922528398 & Range & 32 & Trim Var. & 21.1640894484884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26896&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]41.0553266533066[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]28.7095723988725[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00181085061690[/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]1.97181482469112[/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]5.85483870967742[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.68381008222697[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.0030969131854[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]7.01043411372067[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.06582672108568[/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]4.18969072164948[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.42573358878693[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.7768595041322[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.80059738883268[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.9293940734188[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]13.8412748376943[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.31223628691983[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.64900572969329[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.8116787539808[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.78296750379013[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.2965922528398[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.1640894484884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26896&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26896&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)41.0553266533066Range28Trim Var.28.7095723988725
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.85483870967742Range8Trim Var.2.68381008222697
V(Y[t],d=0,D=1)14.0030969131854Range18Trim Var.7.01043411372067
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)4.18969072164948Range8Trim Var.2.42573358878693
V(Y[t],d=3,D=1)12.7768595041322Range16Trim Var.6.80059738883268
V(Y[t],d=0,D=2)26.9293940734188Range28Trim Var.13.8412748376943
V(Y[t],d=1,D=2)6.31223628691983Range8Trim Var.2.64900572969329
V(Y[t],d=2,D=2)12.8116787539808Range16Trim Var.6.78296750379013
V(Y[t],d=3,D=2)39.2965922528398Range32Trim Var.21.1640894484884


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')