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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 08:44:46 -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/t1228232750wqyhqcitb13hynp.htm/, Retrieved Sun, 19 May 2024 08:46:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27970, Retrieved Sun, 19 May 2024 08:46:21 +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...] [2008-11-29 12:09:03] [74be16979710d4c4e7c6647856088456]
F           [Law of Averages] [law of averages q3] [2008-12-02 15:44:46] [2a6ed4ba8662f0ce2b179e623f45ffb0] [Current]
Feedback Forum
2008-12-06 13:57:44 [Thomas Plasschaert] [reply] 
De VRM gaat trachten om de spreading van de tijdreeks te verkleinen door te differentiëren, d staat voor een gewone differentiatie tewijl D staat voor een seizonale differentiatie. De eerste kolom in de matrix geeft aan hoe vaak er gewoon gedifferentieerd is en hoe vaak seizonaal gedifferentieerd. De 2e kolom geeft de variantie van onze tijdreeks weer, we moeten zoals eerder vermeld kijken naar de kleinste spreiding om een zo stationair mogelijke tijdreeks te bekomen, de optimale spreiding bekomen we bij 1.0018108, dus na 1 keer gewoon te differentiëren en geen enkele keer seizonaal
Als men denkt dat er veel extreme outliers in de tijdreeks zijn, is het beter om naar de getrimde variantie te zien. Ook hier is die het kleinst bij d=1 en D=0.
2008-12-09 22:28:45 [Peter Van Doninck] [reply] 
De student heeft een correcte analyse gemaakt. Het is inderdaad de bedoeling om de variantie zo klein mogelijk te maken. Hoe kleiner deze waarde is, hoe meer je gaat kunnen verklaren. Dit is het geval bij D en d gelijk aan 1. De getrimde variantie gaat geen rekening houden met de zogenaamde outliers, en zal in sommige gevallen een betere benadering geven.

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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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27970&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27970&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27970&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)97.8672384769539Range45Trim Var.54.6316013584921
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.14084507042254Range4Trim Var.0
V(Y[t],d=3,D=0)6.4999350944376Range8Trim Var.2.82292525793249
V(Y[t],d=0,D=1)11.9587807587437Range18Trim Var.4.60843336411203
V(Y[t],d=1,D=1)2.05754556747028Range4Trim Var.0
V(Y[t],d=2,D=1)4.55250943956557Range8Trim Var.2.42075257916393
V(Y[t],d=3,D=1)13.9173553719008Range16Trim Var.6.79552690641474
V(Y[t],d=0,D=2)17.8003361344538Range20Trim Var.9.89937672685215
V(Y[t],d=1,D=2)6.2362691538974Range8Trim Var.2.62024620612683
V(Y[t],d=2,D=2)13.7589673597916Range16Trim Var.6.67678762909871
V(Y[t],d=3,D=2)42.0841007632494Range32Trim Var.22.5733858760896

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 97.8672384769539 & Range & 45 & Trim Var. & 54.6316013584921 \tabularnewline
V(Y[t],d=1,D=0) & 0.99987927662554 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.14084507042254 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.4999350944376 & Range & 8 & Trim Var. & 2.82292525793249 \tabularnewline
V(Y[t],d=0,D=1) & 11.9587807587437 & Range & 18 & Trim Var. & 4.60843336411203 \tabularnewline
V(Y[t],d=1,D=1) & 2.05754556747028 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.55250943956557 & Range & 8 & Trim Var. & 2.42075257916393 \tabularnewline
V(Y[t],d=3,D=1) & 13.9173553719008 & Range & 16 & Trim Var. & 6.79552690641474 \tabularnewline
V(Y[t],d=0,D=2) & 17.8003361344538 & Range & 20 & Trim Var. & 9.89937672685215 \tabularnewline
V(Y[t],d=1,D=2) & 6.2362691538974 & Range & 8 & Trim Var. & 2.62024620612683 \tabularnewline
V(Y[t],d=2,D=2) & 13.7589673597916 & Range & 16 & Trim Var. & 6.67678762909871 \tabularnewline
V(Y[t],d=3,D=2) & 42.0841007632494 & Range & 32 & Trim Var. & 22.5733858760896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27970&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]97.8672384769539[/C][C]Range[/C][C]45[/C][C]Trim Var.[/C][C]54.6316013584921[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99987927662554[/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]2.14084507042254[/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]6.4999350944376[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.82292525793249[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.9587807587437[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.60843336411203[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.05754556747028[/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]4.55250943956557[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.42075257916393[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.9173553719008[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.79552690641474[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]17.8003361344538[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]9.89937672685215[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.2362691538974[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.62024620612683[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.7589673597916[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.67678762909871[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]42.0841007632494[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.5733858760896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27970&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27970&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)97.8672384769539Range45Trim Var.54.6316013584921
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.14084507042254Range4Trim Var.0
V(Y[t],d=3,D=0)6.4999350944376Range8Trim Var.2.82292525793249
V(Y[t],d=0,D=1)11.9587807587437Range18Trim Var.4.60843336411203
V(Y[t],d=1,D=1)2.05754556747028Range4Trim Var.0
V(Y[t],d=2,D=1)4.55250943956557Range8Trim Var.2.42075257916393
V(Y[t],d=3,D=1)13.9173553719008Range16Trim Var.6.79552690641474
V(Y[t],d=0,D=2)17.8003361344538Range20Trim Var.9.89937672685215
V(Y[t],d=1,D=2)6.2362691538974Range8Trim Var.2.62024620612683
V(Y[t],d=2,D=2)13.7589673597916Range16Trim Var.6.67678762909871
V(Y[t],d=3,D=2)42.0841007632494Range32Trim Var.22.5733858760896


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')