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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 computationMon, 01 Dec 2008 19:07:35 -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/t1228184217lavzwl5v93s0pxa.htm/, Retrieved Sun, 19 May 2024 09:21:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27544, Retrieved Sun, 19 May 2024 09:21:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact213

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] [] [2008-12-02 02:07:35] [84e0ffed4a919a8e8c17f955a2802257] [Current]
Feedback Forum
2008-12-07 10:43:48 [Jan Van Riet] [reply] 
De grafiek kan je best als volgt interpreteren:

Kolom 1: Hierin lezen we af van wat de variatie berekend wordt.

d = 0 => het aantal keren dat we niet seizonaal differentiëren
D = 0 => het aantal keren dat we wel seizonaal differentiëren

Kolom 2: De kleinste waarde lezen we af in de tweede rij(1.00055532752251). We gaan hier dus niet seizonaal differentiëren aangezien d=1 en D=0, dit is de meest gunstige waarde.
Kolom 3 + 4: Hier lezen we de range op af.
Kolom 4 + 5: Dit is de getrimde variatie. 5% van de kleinste en grootste waarden worden weggelaten en beïnvloeden bijgevolg het resultaat niet meer.
2008-12-07 16:45:45 [Inge Meelberghs] [reply] 
De Variance reduction matrix techniek wordt gebruikt om de variantie/spreiding te verkleinen om op die manier een zo stationair mogelijke trend te verkrijgen (een tijdreeks zonder trend of verandering van spreiding).
Door differentiatie kan men de variantie laten dalen. Maar men kan op 2 manieren differentiëren, d = gewone differentiatie en D = seizoenale differentiatie. Als we dit eenmaal weten moeten we enkel nog weten hoeveel keer deze differentiatie net moet uitgevoerd worden. Al deze gegevens kunnen we uit de tabel aflezen.

Uit de variance reduction tabel kunnen we zien dat de variantie het kleinst is bij V(Y[t],d=1,D=0) ,namelijk 1.00168207901747. Dit betekent dat als we de reeks 1 keer gewoon differentiëren we het lange termijn effect kunnen uitzuiveren en op die manier een meer stabiel gemiddelde verkrijgen.

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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=27544&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=27544&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27544&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)120.673042084168Range46Trim Var.80.3002096614553
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.91549295774648Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.76023526403273
V(Y[t],d=0,D=1)10.3006025515872Range16Trim Var.5.80818558409279
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)4.04946756607696Range8Trim Var.2.29731477764396
V(Y[t],d=3,D=1)11.9172872113828Range16Trim Var.6.23319809927917
V(Y[t],d=0,D=2)20.1875984077842Range26Trim Var.11.5658473593206
V(Y[t],d=1,D=2)5.89857428381079Range8Trim Var.2.68642659279778
V(Y[t],d=2,D=2)12.1944318070312Range16Trim Var.6.47338577388564
V(Y[t],d=3,D=2)36.1014082488265Range28Trim Var.22.1612733112805

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 120.673042084168 & Range & 46 & Trim Var. & 80.3002096614553 \tabularnewline
V(Y[t],d=1,D=0) & 1.00055532752251 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.91549295774648 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.45966119296424 & Range & 8 & Trim Var. & 2.76023526403273 \tabularnewline
V(Y[t],d=0,D=1) & 10.3006025515872 & Range & 16 & Trim Var. & 5.80818558409279 \tabularnewline
V(Y[t],d=1,D=1) & 1.98352219433670 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.04946756607696 & Range & 8 & Trim Var. & 2.29731477764396 \tabularnewline
V(Y[t],d=3,D=1) & 11.9172872113828 & Range & 16 & Trim Var. & 6.23319809927917 \tabularnewline
V(Y[t],d=0,D=2) & 20.1875984077842 & Range & 26 & Trim Var. & 11.5658473593206 \tabularnewline
V(Y[t],d=1,D=2) & 5.89857428381079 & Range & 8 & Trim Var. & 2.68642659279778 \tabularnewline
V(Y[t],d=2,D=2) & 12.1944318070312 & Range & 16 & Trim Var. & 6.47338577388564 \tabularnewline
V(Y[t],d=3,D=2) & 36.1014082488265 & Range & 28 & Trim Var. & 22.1612733112805 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27544&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]120.673042084168[/C][C]Range[/C][C]46[/C][C]Trim Var.[/C][C]80.3002096614553[/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]1.91549295774648[/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]2.76023526403273[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.3006025515872[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.80818558409279[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.98352219433670[/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]4.04946756607696[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.29731477764396[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.9172872113828[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.23319809927917[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.1875984077842[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]11.5658473593206[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.89857428381079[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.68642659279778[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.1944318070312[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.47338577388564[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.1014082488265[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]22.1612733112805[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27544&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27544&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)120.673042084168Range46Trim Var.80.3002096614553
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.91549295774648Range4Trim Var.0
V(Y[t],d=3,D=0)5.45966119296424Range8Trim Var.2.76023526403273
V(Y[t],d=0,D=1)10.3006025515872Range16Trim Var.5.80818558409279
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)4.04946756607696Range8Trim Var.2.29731477764396
V(Y[t],d=3,D=1)11.9172872113828Range16Trim Var.6.23319809927917
V(Y[t],d=0,D=2)20.1875984077842Range26Trim Var.11.5658473593206
V(Y[t],d=1,D=2)5.89857428381079Range8Trim Var.2.68642659279778
V(Y[t],d=2,D=2)12.1944318070312Range16Trim Var.6.47338577388564
V(Y[t],d=3,D=2)36.1014082488265Range28Trim Var.22.1612733112805


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')