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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 03:42:00 -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/t1228214583pn57iyj60ksbxxo.htm/, Retrieved Fri, 17 May 2024 06:38:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27597, Retrieved Fri, 17 May 2024 06:38:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181

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] [Workshop 4] [2008-12-02 10:42:00] [34b2bf1c29318ebc3536134756a32b87] [Current]
Feedback Forum
2008-12-06 17:38:09 [Stefan Temmerman] [reply] 
De student vergeet hier dat men de variantie kleiner kan maken door te differentiëren. Om de tijdreeks beter te kunnen verklaren, moet de variantie zo klein mogelijk gemaakt worden. Dit wordt bereikt door te differentiëren met d = 1 en D =. De d staat voor het aantal periodes we terug moeten kijken voor de kleinste variantie te bekomen. De D staat op zijn beurt voor het aantal periodes we terug moeten kijken met seizoenaliteit. Deze laatste is gelijk aan nul voor de kleinste variantie te bekomen, omdat we niet moeten kijken naar de seizoenaliteit bij het tossen van een munt.
2008-12-08 18:47:06 [An Knapen] [reply] 
De student heeft hier eigenlijk niets vermeld over de tabel. Deze tabel geeft de waarden van de variantie weer met bijhorende graad van differentiatie. Uit deze tabel moeten we op zoek gaan naar de kleinste waarde. Deze waarde is gelijk aan 1.00181085061690. We moeten enkel niet-seizoenaal differentiëren want kleine d = 1. Dit geldt enkel wanneer men kijkt naar de gewone variantie. Voor de getrimde variantie(=variantie waarbij de extremen zijn weggelaten) is het resultaat echter anders.

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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=27597&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=27597&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27597&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)39.427751503006Range26Trim Var.29.1268775966763
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)2.12474849094567Range4Trim Var.0
V(Y[t],d=3,D=0)6.38709677419355Range8Trim Var.2.89676351046214
V(Y[t],d=0,D=1)10.8693573905140Range16Trim Var.6.282993288741
V(Y[t],d=1,D=1)2.09046737816987Range4Trim Var.0
V(Y[t],d=2,D=1)4.3050867591532Range8Trim Var.2.39578671990637
V(Y[t],d=3,D=1)12.5454545454545Range16Trim Var.6.70674185463659
V(Y[t],d=0,D=2)21.3088544891641Range22Trim Var.13.6851134477034
V(Y[t],d=1,D=2)6.45553630912725Range8Trim Var.2.67586682766948
V(Y[t],d=2,D=2)13.1162612287134Range16Trim Var.6.80931208603843
V(Y[t],d=3,D=2)37.6523811230157Range30Trim Var.21.7440478405975

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 39.427751503006 & Range & 26 & Trim Var. & 29.1268775966763 \tabularnewline
V(Y[t],d=1,D=0) & 1.00181085061690 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.12474849094567 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.38709677419355 & Range & 8 & Trim Var. & 2.89676351046214 \tabularnewline
V(Y[t],d=0,D=1) & 10.8693573905140 & Range & 16 & Trim Var. & 6.282993288741 \tabularnewline
V(Y[t],d=1,D=1) & 2.09046737816987 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.3050867591532 & Range & 8 & Trim Var. & 2.39578671990637 \tabularnewline
V(Y[t],d=3,D=1) & 12.5454545454545 & Range & 16 & Trim Var. & 6.70674185463659 \tabularnewline
V(Y[t],d=0,D=2) & 21.3088544891641 & Range & 22 & Trim Var. & 13.6851134477034 \tabularnewline
V(Y[t],d=1,D=2) & 6.45553630912725 & Range & 8 & Trim Var. & 2.67586682766948 \tabularnewline
V(Y[t],d=2,D=2) & 13.1162612287134 & Range & 16 & Trim Var. & 6.80931208603843 \tabularnewline
V(Y[t],d=3,D=2) & 37.6523811230157 & Range & 30 & Trim Var. & 21.7440478405975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27597&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]39.427751503006[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]29.1268775966763[/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]2.12474849094567[/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]6.38709677419355[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.89676351046214[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.8693573905140[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.282993288741[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09046737816987[/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]4.3050867591532[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.39578671990637[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.5454545454545[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.70674185463659[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.3088544891641[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]13.6851134477034[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.45553630912725[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67586682766948[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.1162612287134[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.80931208603843[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.6523811230157[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]21.7440478405975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27597&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27597&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)39.427751503006Range26Trim Var.29.1268775966763
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)2.12474849094567Range4Trim Var.0
V(Y[t],d=3,D=0)6.38709677419355Range8Trim Var.2.89676351046214
V(Y[t],d=0,D=1)10.8693573905140Range16Trim Var.6.282993288741
V(Y[t],d=1,D=1)2.09046737816987Range4Trim Var.0
V(Y[t],d=2,D=1)4.3050867591532Range8Trim Var.2.39578671990637
V(Y[t],d=3,D=1)12.5454545454545Range16Trim Var.6.70674185463659
V(Y[t],d=0,D=2)21.3088544891641Range22Trim Var.13.6851134477034
V(Y[t],d=1,D=2)6.45553630912725Range8Trim Var.2.67586682766948
V(Y[t],d=2,D=2)13.1162612287134Range16Trim Var.6.80931208603843
V(Y[t],d=3,D=2)37.6523811230157Range30Trim Var.21.7440478405975


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')