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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 computationTue, 02 Dec 2008 13:40:09 -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/t1228250604njsubhw79xj9u8d.htm/, Retrieved Tue, 28 May 2024 12:25:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28417, Retrieved Tue, 28 May 2024 12:25:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJonas Scheltjens
Estimated Impact121

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] [Non Stationary Ti...] [2008-12-02 20:40:09] [f4960a11bac8b7f1cb71c83b5826d5bd] [Current]
Feedback Forum
2008-12-07 09:20:42 [Jolien Van Landeghem] [reply] 
Deze vraag werd ook vrij goed opgelost.
We gaan de variantie van de tijdreeks interpreteren als we het risico zo klein mogelijk wensen te houden (we willen een kleine variantie) deze vinden we voor d=1 en D:0 (logisch want dit werd zo gesimuleerd). De D is gelijk aan nul, want deze geeft aan hoeveel periodes we terug moeten gaan met seizoenaliteit, en dit is logisch aangezien seizoensinvloeden geen rol spelen in dit geval. De d=1 : we moeten 1 periode terugkijken om de kleinste variantie te krijgen en zo de tijdreekst het best kunnen verklaren.
2008-12-07 10:26:51 [Gert-Jan Geudens] [reply] 
Het antwoord van student is correct. We willen nog graag opmerken dat we in het geval van outliers naar de getrimde variantie moeten kijken. De getrimde variantie zorgt ervoor dat de 5% hoogste en laagste gegevens worden verwijderd. De getrimde variantie verwijderd dus het vertekende effect van de outliers. Uiteraard is dit hier niet nodig aangezien er in dit voorbeeld geen sprake is van outliers.

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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 time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28417&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]2 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=28417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28417&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)137.203142284569Range45Trim Var.101.607869124042
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)1.88329979879276Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.62161386293648
V(Y[t],d=0,D=1)13.3031945332750Range20Trim Var.6.56488950095088
V(Y[t],d=1,D=1)1.95776611656146Range4Trim Var.0
V(Y[t],d=2,D=1)3.60410674133469Range8Trim Var.0.943241330502477
V(Y[t],d=3,D=1)10.1735366788788Range16Trim Var.6.47407327469918
V(Y[t],d=0,D=2)26.310959752322Range26Trim Var.12.9923027745813
V(Y[t],d=1,D=2)5.65393737508328Range8Trim Var.2.80325175127562
V(Y[t],d=2,D=2)10.6976565775506Range16Trim Var.5.9166557337945
V(Y[t],d=3,D=2)30.0932024223313Range30Trim Var.16.9302255639098

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 137.203142284569 & Range & 45 & Trim Var. & 101.607869124042 \tabularnewline
V(Y[t],d=1,D=0) & 0.997625773635625 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.88329979879276 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.45966119296424 & Range & 8 & Trim Var. & 2.62161386293648 \tabularnewline
V(Y[t],d=0,D=1) & 13.3031945332750 & Range & 20 & Trim Var. & 6.56488950095088 \tabularnewline
V(Y[t],d=1,D=1) & 1.95776611656146 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.60410674133469 & Range & 8 & Trim Var. & 0.943241330502477 \tabularnewline
V(Y[t],d=3,D=1) & 10.1735366788788 & Range & 16 & Trim Var. & 6.47407327469918 \tabularnewline
V(Y[t],d=0,D=2) & 26.310959752322 & Range & 26 & Trim Var. & 12.9923027745813 \tabularnewline
V(Y[t],d=1,D=2) & 5.65393737508328 & Range & 8 & Trim Var. & 2.80325175127562 \tabularnewline
V(Y[t],d=2,D=2) & 10.6976565775506 & Range & 16 & Trim Var. & 5.9166557337945 \tabularnewline
V(Y[t],d=3,D=2) & 30.0932024223313 & Range & 30 & Trim Var. & 16.9302255639098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28417&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]137.203142284569[/C][C]Range[/C][C]45[/C][C]Trim Var.[/C][C]101.607869124042[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.997625773635625[/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]1.88329979879276[/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]5.45966119296424[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.62161386293648[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.3031945332750[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.56488950095088[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95776611656146[/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]3.60410674133469[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.943241330502477[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.1735366788788[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.47407327469918[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.310959752322[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]12.9923027745813[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.65393737508328[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.80325175127562[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.6976565775506[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.9166557337945[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]30.0932024223313[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]16.9302255639098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28417&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)137.203142284569Range45Trim Var.101.607869124042
V(Y[t],d=1,D=0)0.997625773635625Range2Trim Var.NA
V(Y[t],d=2,D=0)1.88329979879276Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.62161386293648
V(Y[t],d=0,D=1)13.3031945332750Range20Trim Var.6.56488950095088
V(Y[t],d=1,D=1)1.95776611656146Range4Trim Var.0
V(Y[t],d=2,D=1)3.60410674133469Range8Trim Var.0.943241330502477
V(Y[t],d=3,D=1)10.1735366788788Range16Trim Var.6.47407327469918
V(Y[t],d=0,D=2)26.310959752322Range26Trim Var.12.9923027745813
V(Y[t],d=1,D=2)5.65393737508328Range8Trim Var.2.80325175127562
V(Y[t],d=2,D=2)10.6976565775506Range16Trim Var.5.9166557337945
V(Y[t],d=3,D=2)30.0932024223313Range30Trim Var.16.9302255639098


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')