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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 08:25:57 -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/t12282316063cqpsovlrgcwzrz.htm/, Retrieved Sun, 19 May 2024 08:49:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27949, Retrieved Sun, 19 May 2024 08:49:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146

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] [NonStationaryTime...] [2008-12-02 15:25:57] [80e37024345c6a903bf645806b7fbe14] [Current]
Feedback Forum
2008-12-07 19:17:36 [An Knapen] [reply] 
Uit bijhorende tabel moeten we de kleinste waarde halen omdat we de variantie zo klein mogelijk moet zijn.
De grote ‘D’ en de kleine ‘d’ hebben betrekking op het aantal keer dat je differentieert. Je moet dus eerst de kleinste waarde van de variantie zoeken en vervolgens kijken welke ‘D’ en ‘d’ daarbij horen.
In dit geval is de kleinste waarde gelijk aan 1.00110260682007.
De bijhorende waarden van d zijn: d=1 en D=0
We zullen dus enkel niet-seizoenaal moeten differentiëren.

We proberen dus de lange termijn trend weg te werken door een keer te differentiëren(d=1).
2008-12-08 18:40:20 [Sofie Sergoynne] [reply] 
Antwoord van de student is correct, maar er kan nog iets meer informatie bij. We moeten dus idd op zoek gaan naar de variantie met de kleinste waarde. Deze heeft een d=1 en D=0. We moeten dus maar 1 keer gewoon differentiëren (niet seizoenaal)
Zo proberen we dus een lange termijn trend weg te werken!
2008-12-08 19:10:22 [Ellen Van den Broeck] [reply] 
De student antwoorde juist. We kunnen hier nog aan toevoegen dat dus de student een keer moet differentiëren (want d=1) om de lange termijntrend weg te werken.

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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'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27949&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27949&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)40.820745490982Range28Trim Var.28.6762222575348
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.14887719893659Range4Trim Var.0
V(Y[t],d=3,D=0)6.53225806451613Range8Trim Var.2.84481166768383
V(Y[t],d=0,D=1)10.6188945366412Range16Trim Var.5.83378655926933
V(Y[t],d=1,D=1)2.08215242392746Range4Trim Var.0
V(Y[t],d=2,D=1)4.6762716897883Range8Trim Var.2.37159423138344
V(Y[t],d=3,D=1)14.4296839055977Range16Trim Var.6.44991789819376
V(Y[t],d=0,D=2)21.8812030075188Range24Trim Var.13.3897810218978
V(Y[t],d=1,D=2)6.44725738396625Range8Trim Var.2.66855269967224
V(Y[t],d=2,D=2)14.4016734908698Range16Trim Var.7.26260992907801
V(Y[t],d=3,D=2)44.2878489267926Range30Trim Var.30.8771587125416

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 40.820745490982 & Range & 28 & Trim Var. & 28.6762222575348 \tabularnewline
V(Y[t],d=1,D=0) & 1.00152111451819 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.14887719893659 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.53225806451613 & Range & 8 & Trim Var. & 2.84481166768383 \tabularnewline
V(Y[t],d=0,D=1) & 10.6188945366412 & Range & 16 & Trim Var. & 5.83378655926933 \tabularnewline
V(Y[t],d=1,D=1) & 2.08215242392746 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.6762716897883 & Range & 8 & Trim Var. & 2.37159423138344 \tabularnewline
V(Y[t],d=3,D=1) & 14.4296839055977 & Range & 16 & Trim Var. & 6.44991789819376 \tabularnewline
V(Y[t],d=0,D=2) & 21.8812030075188 & Range & 24 & Trim Var. & 13.3897810218978 \tabularnewline
V(Y[t],d=1,D=2) & 6.44725738396625 & Range & 8 & Trim Var. & 2.66855269967224 \tabularnewline
V(Y[t],d=2,D=2) & 14.4016734908698 & Range & 16 & Trim Var. & 7.26260992907801 \tabularnewline
V(Y[t],d=3,D=2) & 44.2878489267926 & Range & 30 & Trim Var. & 30.8771587125416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27949&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]40.820745490982[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]28.6762222575348[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00152111451819[/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]2.14887719893659[/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]6.53225806451613[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.84481166768383[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.6188945366412[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.83378655926933[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.08215242392746[/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]4.6762716897883[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.37159423138344[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]14.4296839055977[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.44991789819376[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.8812030075188[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]13.3897810218978[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.44725738396625[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66855269967224[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]14.4016734908698[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.26260992907801[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]44.2878489267926[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]30.8771587125416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27949&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)40.820745490982Range28Trim Var.28.6762222575348
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.14887719893659Range4Trim Var.0
V(Y[t],d=3,D=0)6.53225806451613Range8Trim Var.2.84481166768383
V(Y[t],d=0,D=1)10.6188945366412Range16Trim Var.5.83378655926933
V(Y[t],d=1,D=1)2.08215242392746Range4Trim Var.0
V(Y[t],d=2,D=1)4.6762716897883Range8Trim Var.2.37159423138344
V(Y[t],d=3,D=1)14.4296839055977Range16Trim Var.6.44991789819376
V(Y[t],d=0,D=2)21.8812030075188Range24Trim Var.13.3897810218978
V(Y[t],d=1,D=2)6.44725738396625Range8Trim Var.2.66855269967224
V(Y[t],d=2,D=2)14.4016734908698Range16Trim Var.7.26260992907801
V(Y[t],d=3,D=2)44.2878489267926Range30Trim Var.30.8771587125416


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')