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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 computationSun, 30 Nov 2008 17:55:33 -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/01/t12280929605yrv4ykztnd2q8m.htm/, Retrieved Sun, 05 May 2024 10:48:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26810, Retrieved Sun, 05 May 2024 10:48:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact252

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] [] [2008-11-30 16:39:37] [4c8dfb519edec2da3492d7e6be9a5685]
F           [Law of Averages] [Q3] [2008-12-01 00:55:33] [e81ac192d6ae6d77191d83851a692999] [Current]
Feedback Forum
2008-12-08 00:38:42 [Gregory Van Overmeiren] [reply] 
De Variance Reduction Matrix heb je nodig om verschillende differentiatie waarden op een tijdreeks te zoeken en ze toont de daarbij gerelateerde variatie. Waar de variatie het kleinst is, noteren we het meest adequate stationaire karakter. Door de lange termijn trend zo klein mogelijk te maken, kunnen we zoveel mogelijk van de tijdreeks verklaren. We moesten hier dus de optimale d en D te indentificeren. We zien dan de waarde van d en D optimaal is bij 1.
2008-12-08 22:57:22 [Gregory Van Overmeiren] [reply] 
Correctie : We zien dan de waarde van d=1 en D=0 optimaal is.

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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=26810&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=26810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26810&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)28.8216432865731Range24Trim Var.17.9900998890122
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)2.04426559356137Range4Trim Var.0
V(Y[t],d=3,D=0)6.12095151554488Range8Trim Var.2.75672761710498
V(Y[t],d=0,D=1)11.6796714579055Range16Trim Var.6.66348448687351
V(Y[t],d=1,D=1)1.80231703298096Range4Trim Var.0
V(Y[t],d=2,D=1)3.57111705061304Range8Trim Var.0
V(Y[t],d=3,D=1)10.5950413223140Range16Trim Var.6.40066592674806
V(Y[t],d=0,D=2)20.6953383458647Range26Trim Var.11.4683637705220
V(Y[t],d=1,D=2)5.39224516988674Range8Trim Var.2.40845049901654
V(Y[t],d=2,D=2)10.7567996717246Range16Trim Var.6.42224681793027
V(Y[t],d=3,D=2)31.9830508474576Range32Trim Var.19.5170547327312

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 28.8216432865731 & Range & 24 & Trim Var. & 17.9900998890122 \tabularnewline
V(Y[t],d=1,D=0) & 1.00200400801603 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.04426559356137 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.12095151554488 & Range & 8 & Trim Var. & 2.75672761710498 \tabularnewline
V(Y[t],d=0,D=1) & 11.6796714579055 & Range & 16 & Trim Var. & 6.66348448687351 \tabularnewline
V(Y[t],d=1,D=1) & 1.80231703298096 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.57111705061304 & Range & 8 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=1) & 10.5950413223140 & Range & 16 & Trim Var. & 6.40066592674806 \tabularnewline
V(Y[t],d=0,D=2) & 20.6953383458647 & Range & 26 & Trim Var. & 11.4683637705220 \tabularnewline
V(Y[t],d=1,D=2) & 5.39224516988674 & Range & 8 & Trim Var. & 2.40845049901654 \tabularnewline
V(Y[t],d=2,D=2) & 10.7567996717246 & Range & 16 & Trim Var. & 6.42224681793027 \tabularnewline
V(Y[t],d=3,D=2) & 31.9830508474576 & Range & 32 & Trim Var. & 19.5170547327312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26810&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]28.8216432865731[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]17.9900998890122[/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]2.04426559356137[/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]6.12095151554488[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.75672761710498[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.6796714579055[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.66348448687351[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.80231703298096[/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]3.57111705061304[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.5950413223140[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.40066592674806[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.6953383458647[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]11.4683637705220[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.39224516988674[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.40845049901654[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.7567996717246[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.42224681793027[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]31.9830508474576[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]19.5170547327312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26810&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)28.8216432865731Range24Trim Var.17.9900998890122
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)2.04426559356137Range4Trim Var.0
V(Y[t],d=3,D=0)6.12095151554488Range8Trim Var.2.75672761710498
V(Y[t],d=0,D=1)11.6796714579055Range16Trim Var.6.66348448687351
V(Y[t],d=1,D=1)1.80231703298096Range4Trim Var.0
V(Y[t],d=2,D=1)3.57111705061304Range8Trim Var.0
V(Y[t],d=3,D=1)10.5950413223140Range16Trim Var.6.40066592674806
V(Y[t],d=0,D=2)20.6953383458647Range26Trim Var.11.4683637705220
V(Y[t],d=1,D=2)5.39224516988674Range8Trim Var.2.40845049901654
V(Y[t],d=2,D=2)10.7567996717246Range16Trim Var.6.42224681793027
V(Y[t],d=3,D=2)31.9830508474576Range32Trim Var.19.5170547327312


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')