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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 computationMon, 01 Dec 2008 13:51:54 -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/t1228164753259odayuxjjxfu4.htm/, Retrieved Sun, 05 May 2024 14:55:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27391, Retrieved Sun, 05 May 2024 14:55:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171

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] [Q3 - 1ste reprodu...] [2008-12-01 20:51:54] [8da7502cfecb272886bc60b3f290b8b8] [Current]
-           [Law of Averages] [Q3 - 2de reproduc...] [2008-12-01 20:53:14] [9e54d1454d464f1bf9ee4a54d5d56945]
Feedback Forum
2008-12-08 18:42:31 [Evelien Blockx] [reply] 
Hier vond ik enkel de berekeningen, en geen interpretatie of antwoord.

In de tabel moet je op zoek gaan naar de kleinste variantie. Deze wordt gevonden bij d=1, D=0. De variantie is daar 1.00084506362122.

Daarna werken we verder met de d en D bij onze kleinst gevonden variantie.
d= gewone differentiatie
D= seizoenale differentiatie

Deze gegevens zullen we nodig hebben om de tijdreeks stationair te maken.

In dit geval moeten we dus 1 keer gewoon differentiëren (d=1) en helemaal niet seizoenaal differentiëren (D=0). Dan houd je de variantie zo klein mogelijk.

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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=27391&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=27391&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27391&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)20.1612985971944Range20Trim Var.13.9760805014847
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.26611280586746Range8Trim Var.2.76394939740999
V(Y[t],d=0,D=1)10.6444272393712Range16Trim Var.5.73759453975281
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)4.10721649484536Range8Trim Var.0.96338028169014
V(Y[t],d=3,D=1)12.2892391582176Range16Trim Var.7.04209214248046
V(Y[t],d=0,D=2)23.9711985846970Range28Trim Var.13.2966733564435
V(Y[t],d=1,D=2)6.14338885187653Range8Trim Var.2.68894068894069
V(Y[t],d=2,D=2)12.3805496828753Range16Trim Var.7.00847263567667
V(Y[t],d=3,D=2)36.9829791808507Range32Trim Var.23.037987185046

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 20.1612985971944 & Range & 20 & Trim Var. & 13.9760805014847 \tabularnewline
V(Y[t],d=1,D=0) & 1.00084506362122 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.07645875251509 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.26611280586746 & Range & 8 & Trim Var. & 2.76394939740999 \tabularnewline
V(Y[t],d=0,D=1) & 10.6444272393712 & Range & 16 & Trim Var. & 5.73759453975281 \tabularnewline
V(Y[t],d=1,D=1) & 2.02462375677069 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.10721649484536 & Range & 8 & Trim Var. & 0.96338028169014 \tabularnewline
V(Y[t],d=3,D=1) & 12.2892391582176 & Range & 16 & Trim Var. & 7.04209214248046 \tabularnewline
V(Y[t],d=0,D=2) & 23.9711985846970 & Range & 28 & Trim Var. & 13.2966733564435 \tabularnewline
V(Y[t],d=1,D=2) & 6.14338885187653 & Range & 8 & Trim Var. & 2.68894068894069 \tabularnewline
V(Y[t],d=2,D=2) & 12.3805496828753 & Range & 16 & Trim Var. & 7.00847263567667 \tabularnewline
V(Y[t],d=3,D=2) & 36.9829791808507 & Range & 32 & Trim Var. & 23.037987185046 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27391&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]20.1612985971944[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]13.9760805014847[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00084506362122[/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]2.07645875251509[/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]6.26611280586746[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.76394939740999[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.6444272393712[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.73759453975281[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.02462375677069[/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]4.10721649484536[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.96338028169014[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.2892391582176[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.04209214248046[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.9711985846970[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]13.2966733564435[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.14338885187653[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.68894068894069[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.3805496828753[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.00847263567667[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.9829791808507[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]23.037987185046[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27391&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27391&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)20.1612985971944Range20Trim Var.13.9760805014847
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.26611280586746Range8Trim Var.2.76394939740999
V(Y[t],d=0,D=1)10.6444272393712Range16Trim Var.5.73759453975281
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)4.10721649484536Range8Trim Var.0.96338028169014
V(Y[t],d=3,D=1)12.2892391582176Range16Trim Var.7.04209214248046
V(Y[t],d=0,D=2)23.9711985846970Range28Trim Var.13.2966733564435
V(Y[t],d=1,D=2)6.14338885187653Range8Trim Var.2.68894068894069
V(Y[t],d=2,D=2)12.3805496828753Range16Trim Var.7.00847263567667
V(Y[t],d=3,D=2)36.9829791808507Range32Trim Var.23.037987185046


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')