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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 computationFri, 28 Nov 2008 05:43:28 -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/Nov/28/t1227876354x1ros6e9202r4e5.htm/, Retrieved Sun, 19 May 2024 12:19:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26053, Retrieved Sun, 19 May 2024 12:19:46 +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] [Variance Reductio...] [2008-11-28 12:43:28] [98255691c21504803b38711776845ae0] [Current]
Feedback Forum
2008-12-06 13:42:27 [Natalie De Wilde] [reply] 
Goed, nog enkele aanvullingen
In de tweede kolom zien we inderdaad de variantie, dit is de tijdreeks nadat deze een aantal keer gedifferentieerd is. D is seizoenaal differentiëren en d is niet seizoenaal differentiëren (wordt inderdaad gebruikt om de lange termijn trend weg te werken).
We moeten zoeken naar de kleinst mogelijk variantie, hoe kleiner deze is, hoe meer we kunnen verklaren.
Hier zien we de kleinste variantie bij d=1 en D=0. We kunnen ook kijken naar de Trim Var, hier moeten we opnieuw op zoek gaan naar de kleinste waarde, dikwijls komt dit overeen met de Variantie. In deze tabel staat er bij d=1 en D=0 geen Trim Var weergegeven.

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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=26053&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=26053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26053&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)46.5186533066132Range31Trim Var.28.8986650051582
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)6.11290322580645Range8Trim Var.2.56138932554832
V(Y[t],d=0,D=1)12.3635338472414Range20Trim Var.6.32662099985084
V(Y[t],d=1,D=1)1.97530864197531Range4Trim Var.0
V(Y[t],d=2,D=1)4.03297272071613Range8Trim Var.2.27519068647130
V(Y[t],d=3,D=1)12.3470392774985Range16Trim Var.6.11192019950125
V(Y[t],d=0,D=2)22.6770278637771Range28Trim Var.12.5832192862407
V(Y[t],d=1,D=2)5.8227137463913Range8Trim Var.2.664170585818
V(Y[t],d=2,D=2)12.0760385723589Range16Trim Var.6.5681809551536
V(Y[t],d=3,D=2)36.8898125918228Range32Trim Var.22.1949757898269

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 46.5186533066132 & Range & 31 & Trim Var. & 28.8986650051582 \tabularnewline
V(Y[t],d=1,D=0) & 1.00110260682007 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.00400798364484 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.11290322580645 & Range & 8 & Trim Var. & 2.56138932554832 \tabularnewline
V(Y[t],d=0,D=1) & 12.3635338472414 & Range & 20 & Trim Var. & 6.32662099985084 \tabularnewline
V(Y[t],d=1,D=1) & 1.97530864197531 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.03297272071613 & Range & 8 & Trim Var. & 2.27519068647130 \tabularnewline
V(Y[t],d=3,D=1) & 12.3470392774985 & Range & 16 & Trim Var. & 6.11192019950125 \tabularnewline
V(Y[t],d=0,D=2) & 22.6770278637771 & Range & 28 & Trim Var. & 12.5832192862407 \tabularnewline
V(Y[t],d=1,D=2) & 5.8227137463913 & Range & 8 & Trim Var. & 2.664170585818 \tabularnewline
V(Y[t],d=2,D=2) & 12.0760385723589 & Range & 16 & Trim Var. & 6.5681809551536 \tabularnewline
V(Y[t],d=3,D=2) & 36.8898125918228 & Range & 32 & Trim Var. & 22.1949757898269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26053&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]46.5186533066132[/C][C]Range[/C][C]31[/C][C]Trim Var.[/C][C]28.8986650051582[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00110260682007[/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]2.00400798364484[/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]6.11290322580645[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.56138932554832[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.3635338472414[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.32662099985084[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.97530864197531[/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]4.03297272071613[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.27519068647130[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.3470392774985[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.11192019950125[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]22.6770278637771[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.5832192862407[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.8227137463913[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.664170585818[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.0760385723589[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.5681809551536[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.8898125918228[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.1949757898269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26053&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)46.5186533066132Range31Trim Var.28.8986650051582
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)6.11290322580645Range8Trim Var.2.56138932554832
V(Y[t],d=0,D=1)12.3635338472414Range20Trim Var.6.32662099985084
V(Y[t],d=1,D=1)1.97530864197531Range4Trim Var.0
V(Y[t],d=2,D=1)4.03297272071613Range8Trim Var.2.27519068647130
V(Y[t],d=3,D=1)12.3470392774985Range16Trim Var.6.11192019950125
V(Y[t],d=0,D=2)22.6770278637771Range28Trim Var.12.5832192862407
V(Y[t],d=1,D=2)5.8227137463913Range8Trim Var.2.664170585818
V(Y[t],d=2,D=2)12.0760385723589Range16Trim Var.6.5681809551536
V(Y[t],d=3,D=2)36.8898125918228Range32Trim Var.22.1949757898269


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')