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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 computationSat, 29 Nov 2008 13:58:37 -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/29/t1227992375uz2bpllzhqbdzl4.htm/, Retrieved Sun, 19 May 2024 04:12:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26377, Retrieved Sun, 19 May 2024 04:12:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Dooren Leen
Estimated Impact152

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...] [2008-11-29 20:58:37] [d175f84d503eb4f2a43145d5e67795b5] [Current]
Feedback Forum
2008-12-06 19:24:50 [Stefan Temmerman] [reply] 
Om de tijdreeks beter te kunnen verklaren, probeert de student correct de variantie zo klein mogelijk te maken. Dit wordt bereikt door te differentiëren met d = 1 en D =. De d staat voor het aantal periodes we terug moeten kijken voor de kleinste variantie te bekomen. De D staat op zijn beurt voor het aantal periodes we terug moeten kijken met seizoenaliteit. Deze laatste is gelijk aan nul voor de kleinste variantie te bekomen, omdat we niet moeten kijken naar de seizoenaliteit bij het tossen van een munt.
2008-12-07 10:58:36 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
Goed opgelost en de tabel juist geïnterpreteerd.
2008-12-07 11:49:53 [Lana Van Wesemael] [reply] 
Goed opgelost. In de tabel staat ook een getrimde variantie gegeven. Indien er veel outliers zijn is het een goed idee om de getrimde variantie te gebruiken in plaats van de gewone.
2008-12-08 18:57:31 [Birgit Van Dyck] [reply] 
Goede oplossing en uitgebreide interpretatie

Post a new message

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=26377&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=26377&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26377&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)184.463470941884Range55Trim Var.130.093713938658
V(Y[t],d=1,D=0)0.99456744814931Range2Trim Var.NA
V(Y[t],d=2,D=0)2.03620114259856Range4Trim Var.0
V(Y[t],d=3,D=0)6.16933861231908Range8Trim Var.2.66898944327809
V(Y[t],d=0,D=1)10.9525701013229Range20Trim Var.4.11315955068214
V(Y[t],d=1,D=1)1.92565552090991Range4Trim Var.0
V(Y[t],d=2,D=1)4.22268041237113Range8Trim Var.2.29297901391805
V(Y[t],d=3,D=1)13.1404958677686Range16Trim Var.6.50719592926851
V(Y[t],d=0,D=2)21.8534630694383Range28Trim Var.12.7013794307665
V(Y[t],d=1,D=2)5.66228736397957Range8Trim Var.2.62359317616396
V(Y[t],d=2,D=2)12.7610815246965Range16Trim Var.6.60787765854912
V(Y[t],d=3,D=2)40.2200523166231Range32Trim Var.21.1438946426288

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 184.463470941884 & Range & 55 & Trim Var. & 130.093713938658 \tabularnewline
V(Y[t],d=1,D=0) & 0.99456744814931 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.03620114259856 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.16933861231908 & Range & 8 & Trim Var. & 2.66898944327809 \tabularnewline
V(Y[t],d=0,D=1) & 10.9525701013229 & Range & 20 & Trim Var. & 4.11315955068214 \tabularnewline
V(Y[t],d=1,D=1) & 1.92565552090991 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.22268041237113 & Range & 8 & Trim Var. & 2.29297901391805 \tabularnewline
V(Y[t],d=3,D=1) & 13.1404958677686 & Range & 16 & Trim Var. & 6.50719592926851 \tabularnewline
V(Y[t],d=0,D=2) & 21.8534630694383 & Range & 28 & Trim Var. & 12.7013794307665 \tabularnewline
V(Y[t],d=1,D=2) & 5.66228736397957 & Range & 8 & Trim Var. & 2.62359317616396 \tabularnewline
V(Y[t],d=2,D=2) & 12.7610815246965 & Range & 16 & Trim Var. & 6.60787765854912 \tabularnewline
V(Y[t],d=3,D=2) & 40.2200523166231 & Range & 32 & Trim Var. & 21.1438946426288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26377&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]184.463470941884[/C][C]Range[/C][C]55[/C][C]Trim Var.[/C][C]130.093713938658[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99456744814931[/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]2.03620114259856[/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]6.16933861231908[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66898944327809[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.9525701013229[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]4.11315955068214[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.92565552090991[/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]4.22268041237113[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.29297901391805[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.1404958677686[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.50719592926851[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.8534630694383[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.7013794307665[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.66228736397957[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.62359317616396[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.7610815246965[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.60787765854912[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]40.2200523166231[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.1438946426288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26377&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26377&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)184.463470941884Range55Trim Var.130.093713938658
V(Y[t],d=1,D=0)0.99456744814931Range2Trim Var.NA
V(Y[t],d=2,D=0)2.03620114259856Range4Trim Var.0
V(Y[t],d=3,D=0)6.16933861231908Range8Trim Var.2.66898944327809
V(Y[t],d=0,D=1)10.9525701013229Range20Trim Var.4.11315955068214
V(Y[t],d=1,D=1)1.92565552090991Range4Trim Var.0
V(Y[t],d=2,D=1)4.22268041237113Range8Trim Var.2.29297901391805
V(Y[t],d=3,D=1)13.1404958677686Range16Trim Var.6.50719592926851
V(Y[t],d=0,D=2)21.8534630694383Range28Trim Var.12.7013794307665
V(Y[t],d=1,D=2)5.66228736397957Range8Trim Var.2.62359317616396
V(Y[t],d=2,D=2)12.7610815246965Range16Trim Var.6.60787765854912
V(Y[t],d=3,D=2)40.2200523166231Range32Trim Var.21.1438946426288


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')