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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 06:53:21 -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/t122822602183yjdkkm0ae3nz7.htm/, Retrieved Sun, 19 May 2024 08:51:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27795, Retrieved Sun, 19 May 2024 08:51:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186

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 13:53:21] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMPD      [Variance Reduction Matrix] [Non stationary] [2008-12-08 18:11:10] [072df11bdb18ed8d65d8164df87f26f2]
Feedback Forum
2008-12-07 13:06:09 [Käthe Vanderheggen] [reply] 
De student maakte een foute berekening: kies de module 'variance reduction matrix' aan de rechterkant van de calculator en kies als seizoenale periode 12. Dan zie je de matrix die aantoont dat de kleinste en beste variantie die bij d=1,D=1 is.
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/06/t122856388449a43xdmp1j4mh4.htm
De variance reduction matrix zorgt ervoor dat de variantie verkleint en er dus meer kan worden verklaard. Het differentieert eerst de tijdreeks en berekent dan de variantie. We hebben dus de seizoenale en niet-seizoenale trend verwijderd.
We zouden ook kunnen kijken naar de getrimde variantie. Dat bekomen we door na de differentiatie de extremen weg te laten en dan opnieuw de variantie te berekenen. Die is toevallig ook het kleinste voor d=1 D=1.
2008-12-08 18:18:07 [Erik Geysen] [reply] 
Ik heb dit gereproduceerd.
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/08/t1228759962jk185sdv1n2qjqw.htm

seasonal period = 12
D= seizoenaal differentiëren, dit gebruiken we om de seizoenaliteit uit een tijdreeks te verwijderen. d= het aantal keer dat gedifferentieerd wordt. De V staat voor de variantie en deze is de variantie nadat de differentiatie is gebeurd. We kunnen het meeste verklaren als de variantie klein is. Bij de kleinste variantie is d = 1 en D = 1. Dit is dus een andere uitkomst als de student. We kunnen ook naar de getrimde variantie kijken. Hier zijn de outliers weg gewerkt. Ook deze is het kleinst bij d = 1 en D = 1. 0.

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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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27795&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27795&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)101.510124248497Range40Trim Var.76.4119917367864
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.99993509443759Range8Trim Var.2.48311811396754
V(Y[t],d=0,D=1)14.9893122833002Range22Trim Var.6.63977317317064
V(Y[t],d=1,D=1)1.90121766758773Range4Trim Var.0
V(Y[t],d=2,D=1)3.69484536082474Range8Trim Var.0.94911786198977
V(Y[t],d=3,D=1)11.4297350259862Range16Trim Var.6.60725390979083
V(Y[t],d=0,D=2)27.4828482972136Range30Trim Var.16.0275354578363
V(Y[t],d=1,D=2)5.63684654674661Range8Trim Var.2.53659705067745
V(Y[t],d=2,D=2)10.9598308668076Range16Trim Var.6.10085272133909
V(Y[t],d=3,D=2)34.0508474576271Range32Trim Var.17.4210372883153

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 101.510124248497 & Range & 40 & Trim Var. & 76.4119917367864 \tabularnewline
V(Y[t],d=1,D=0) & 1.00200400801603 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.96378269617706 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.99993509443759 & Range & 8 & Trim Var. & 2.48311811396754 \tabularnewline
V(Y[t],d=0,D=1) & 14.9893122833002 & Range & 22 & Trim Var. & 6.63977317317064 \tabularnewline
V(Y[t],d=1,D=1) & 1.90121766758773 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.69484536082474 & Range & 8 & Trim Var. & 0.94911786198977 \tabularnewline
V(Y[t],d=3,D=1) & 11.4297350259862 & Range & 16 & Trim Var. & 6.60725390979083 \tabularnewline
V(Y[t],d=0,D=2) & 27.4828482972136 & Range & 30 & Trim Var. & 16.0275354578363 \tabularnewline
V(Y[t],d=1,D=2) & 5.63684654674661 & Range & 8 & Trim Var. & 2.53659705067745 \tabularnewline
V(Y[t],d=2,D=2) & 10.9598308668076 & Range & 16 & Trim Var. & 6.10085272133909 \tabularnewline
V(Y[t],d=3,D=2) & 34.0508474576271 & Range & 32 & Trim Var. & 17.4210372883153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27795&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]101.510124248497[/C][C]Range[/C][C]40[/C][C]Trim Var.[/C][C]76.4119917367864[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00200400801603[/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]1.96378269617706[/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]5.99993509443759[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.48311811396754[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.9893122833002[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]6.63977317317064[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.90121766758773[/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]3.69484536082474[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.94911786198977[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.4297350259862[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.60725390979083[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]27.4828482972136[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]16.0275354578363[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.63684654674661[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.53659705067745[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.9598308668076[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.10085272133909[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.0508474576271[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]17.4210372883153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27795&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)101.510124248497Range40Trim Var.76.4119917367864
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.96378269617706Range4Trim Var.0
V(Y[t],d=3,D=0)5.99993509443759Range8Trim Var.2.48311811396754
V(Y[t],d=0,D=1)14.9893122833002Range22Trim Var.6.63977317317064
V(Y[t],d=1,D=1)1.90121766758773Range4Trim Var.0
V(Y[t],d=2,D=1)3.69484536082474Range8Trim Var.0.94911786198977
V(Y[t],d=3,D=1)11.4297350259862Range16Trim Var.6.60725390979083
V(Y[t],d=0,D=2)27.4828482972136Range30Trim Var.16.0275354578363
V(Y[t],d=1,D=2)5.63684654674661Range8Trim Var.2.53659705067745
V(Y[t],d=2,D=2)10.9598308668076Range16Trim Var.6.10085272133909
V(Y[t],d=3,D=2)34.0508474576271Range32Trim Var.17.4210372883153


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')