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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 computationFri, 28 Nov 2008 05:59:15 -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/28/t1227877182n7h8gajpcvqa85d.htm/, Retrieved Sun, 19 May 2024 09:09:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26065, Retrieved Sun, 19 May 2024 09:09:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178

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 - random walk] [2008-11-28 12:59:15] [2ae5313507f69e6db9a3a7e1ca4e6147] [Current]
Feedback Forum
2008-12-06 16:37:35 [Kevin Engels] [reply] 
De student geeft het correcte antwoord. Op de Variance Reduction Matrix zien we in de eerste kolom V(Y[t],d=0,D=0) staan: dit is de variantie van functie Y(t) nadat je x aantal keer differentieert(= waarde van d aanpassen). De tweede kolom geeft de spreiding van de reeks weer. Wanneer we een eerste keer gingen differentiëren, hoopten we dat de eerste variantie van 54 zou verkleinen. Bij d=1 kwam men dan ook tot een waarde van 1,0005.
2008-12-07 12:31:01 [Kevin Neelen] [reply] 
Het antwoord van de studente is juist. Hier zoeken we meer bepaald naar een ideaal aantal graden van gewone differentiatie (d) en seizoensdifferentiatie (D). Deze wordt bereikt wanneer de variantie (kolom 2) het kleinst is. Deze module maakt de berekeningen en in deze tabel kunnen we zien dat de variantie het kleinst bij d=1 en D=0. Hier is de variantie dus stationair.

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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=26065&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=26065&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26065&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)67.7278557114228Range32Trim Var.53.052161149914
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.87523534782995Range4Trim Var.0
V(Y[t],d=3,D=0)5.41935483870968Range8Trim Var.2.61182946461027
V(Y[t],d=0,D=1)10.6010704547750Range18Trim Var.4.61903134526267
V(Y[t],d=1,D=1)2.01644400503629Range4Trim Var.0
V(Y[t],d=2,D=1)3.61237113402062Range8Trim Var.0.894679695982628
V(Y[t],d=3,D=1)10.1900656044986Range16Trim Var.5.70777997282205
V(Y[t],d=0,D=2)24.1827156125608Range28Trim Var.12.2200329214063
V(Y[t],d=1,D=2)6.09218743060182Range8Trim Var.2.69637169699589
V(Y[t],d=2,D=2)10.8498764507007Range16Trim Var.6.23841920015118
V(Y[t],d=3,D=2)30.2881355932203Range28Trim Var.19.4526955270580

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 67.7278557114228 & Range & 32 & Trim Var. & 53.052161149914 \tabularnewline
V(Y[t],d=1,D=0) & 1.00055532752251 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.87523534782995 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.41935483870968 & Range & 8 & Trim Var. & 2.61182946461027 \tabularnewline
V(Y[t],d=0,D=1) & 10.6010704547750 & Range & 18 & Trim Var. & 4.61903134526267 \tabularnewline
V(Y[t],d=1,D=1) & 2.01644400503629 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.61237113402062 & Range & 8 & Trim Var. & 0.894679695982628 \tabularnewline
V(Y[t],d=3,D=1) & 10.1900656044986 & Range & 16 & Trim Var. & 5.70777997282205 \tabularnewline
V(Y[t],d=0,D=2) & 24.1827156125608 & Range & 28 & Trim Var. & 12.2200329214063 \tabularnewline
V(Y[t],d=1,D=2) & 6.09218743060182 & Range & 8 & Trim Var. & 2.69637169699589 \tabularnewline
V(Y[t],d=2,D=2) & 10.8498764507007 & Range & 16 & Trim Var. & 6.23841920015118 \tabularnewline
V(Y[t],d=3,D=2) & 30.2881355932203 & Range & 28 & Trim Var. & 19.4526955270580 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26065&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]67.7278557114228[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]53.052161149914[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00055532752251[/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]1.87523534782995[/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]5.41935483870968[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.61182946461027[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.6010704547750[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.61903134526267[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.01644400503629[/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]3.61237113402062[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.894679695982628[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.1900656044986[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.70777997282205[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.1827156125608[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.2200329214063[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.09218743060182[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69637169699589[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.8498764507007[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.23841920015118[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]30.2881355932203[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]19.4526955270580[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26065&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26065&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)67.7278557114228Range32Trim Var.53.052161149914
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.87523534782995Range4Trim Var.0
V(Y[t],d=3,D=0)5.41935483870968Range8Trim Var.2.61182946461027
V(Y[t],d=0,D=1)10.6010704547750Range18Trim Var.4.61903134526267
V(Y[t],d=1,D=1)2.01644400503629Range4Trim Var.0
V(Y[t],d=2,D=1)3.61237113402062Range8Trim Var.0.894679695982628
V(Y[t],d=3,D=1)10.1900656044986Range16Trim Var.5.70777997282205
V(Y[t],d=0,D=2)24.1827156125608Range28Trim Var.12.2200329214063
V(Y[t],d=1,D=2)6.09218743060182Range8Trim Var.2.69637169699589
V(Y[t],d=2,D=2)10.8498764507007Range16Trim Var.6.23841920015118
V(Y[t],d=3,D=2)30.2881355932203Range28Trim Var.19.4526955270580


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')