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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 08:47:22 -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/t1228146595w9q7loujsqqgn7t.htm/, Retrieved Sun, 05 May 2024 19:54:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26957, Retrieved Sun, 05 May 2024 19:54:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact222

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] [Random Walk Simul...] [2008-11-27 19:16:25] [58bf45a666dc5198906262e8815a9722]
F           [Law of Averages] [] [2008-12-01 15:47:22] [7ed4ec9f8cdf7df79ef87b9dc09dff20] [Current]
Feedback Forum
2008-12-03 09:58:26 [Romina Machiels] [reply] 
Deze vraag werd wel berekend maar er werd geen uitleg gegeven.
In de tabel verbetert de variantie (= de grootte van de spreiding) wanneer we 1 keer gewoon differentiëren, dus wanneer d=1 en D=0. We kunnen dit aflezen doordat de waarde in de tweede kolom hier het kleinste is, en wanneer we een voorspelling doen wensen we het niet verklaarde deel (de variantie) zo klein mogelijk te houden.
2008-12-08 18:02:50 [Jeroen Aerts] [reply] 
Om naar een stationair karakter over te gaan mag er geen seizoenaliteit, noch een trend zijn, omdat dan de variantie het kleinst zal zijn.

De tabel toont aan dat dit bij d= 1 en D= 0 zich voortdoet: daar is de variantie namelijk : 0.99987927662554.

d = het aantal keer dat de reeks niet-seizoenaal gedifferentieerd is.
D = het aantal keer dat de reeks seizoenaal gedifferentieerd is.

Dit toont deze berekening ook aan, maar er werd geen uitleg gegeven bij de tabel
2008-12-08 18:53:37 [Yara Van Overstraeten] [reply] 
Het is inderdaad jammer dat enkel de berekening werd gemaakt zonder verdere interpretatie. Aan de feedback van Jeroen kan ik niets meer aan toevoegen.

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=26957&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=26957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26957&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)70.8625891783567Range33Trim Var.52.3355893422291
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.08449088102915Range4Trim Var.0
V(Y[t],d=3,D=0)6.35483870967742Range8Trim Var.2.70914127423823
V(Y[t],d=0,D=1)10.3388258659575Range16Trim Var.4.5638015689373
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)3.95049849391201Range8Trim Var.2.24938967136150
V(Y[t],d=3,D=1)11.9834029138621Range16Trim Var.6.24422362353397
V(Y[t],d=0,D=2)25.1696594427245Range30Trim Var.14.0314492545184
V(Y[t],d=1,D=2)5.85654008438819Range8Trim Var.2.71628388353652
V(Y[t],d=2,D=2)11.5010570824524Range16Trim Var.6.19250381508914
V(Y[t],d=3,D=2)34.9066184111513Range28Trim Var.20.478594371734

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 70.8625891783567 & Range & 33 & Trim Var. & 52.3355893422291 \tabularnewline
V(Y[t],d=1,D=0) & 0.99987927662554 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.08449088102915 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.35483870967742 & Range & 8 & Trim Var. & 2.70914127423823 \tabularnewline
V(Y[t],d=0,D=1) & 10.3388258659575 & Range & 16 & Trim Var. & 4.5638015689373 \tabularnewline
V(Y[t],d=1,D=1) & 1.98352219433670 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.95049849391201 & Range & 8 & Trim Var. & 2.24938967136150 \tabularnewline
V(Y[t],d=3,D=1) & 11.9834029138621 & Range & 16 & Trim Var. & 6.24422362353397 \tabularnewline
V(Y[t],d=0,D=2) & 25.1696594427245 & Range & 30 & Trim Var. & 14.0314492545184 \tabularnewline
V(Y[t],d=1,D=2) & 5.85654008438819 & Range & 8 & Trim Var. & 2.71628388353652 \tabularnewline
V(Y[t],d=2,D=2) & 11.5010570824524 & Range & 16 & Trim Var. & 6.19250381508914 \tabularnewline
V(Y[t],d=3,D=2) & 34.9066184111513 & Range & 28 & Trim Var. & 20.478594371734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26957&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]70.8625891783567[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]52.3355893422291[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99987927662554[/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]2.08449088102915[/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]6.35483870967742[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.70914127423823[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.3388258659575[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.5638015689373[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.98352219433670[/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]3.95049849391201[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.24938967136150[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.9834029138621[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.24422362353397[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.1696594427245[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]14.0314492545184[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.85654008438819[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.71628388353652[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.5010570824524[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.19250381508914[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.9066184111513[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]20.478594371734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26957&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)70.8625891783567Range33Trim Var.52.3355893422291
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.08449088102915Range4Trim Var.0
V(Y[t],d=3,D=0)6.35483870967742Range8Trim Var.2.70914127423823
V(Y[t],d=0,D=1)10.3388258659575Range16Trim Var.4.5638015689373
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)3.95049849391201Range8Trim Var.2.24938967136150
V(Y[t],d=3,D=1)11.9834029138621Range16Trim Var.6.24422362353397
V(Y[t],d=0,D=2)25.1696594427245Range30Trim Var.14.0314492545184
V(Y[t],d=1,D=2)5.85654008438819Range8Trim Var.2.71628388353652
V(Y[t],d=2,D=2)11.5010570824524Range16Trim Var.6.19250381508914
V(Y[t],d=3,D=2)34.9066184111513Range28Trim Var.20.478594371734


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')