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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 computationMon, 01 Dec 2008 09:35:41 -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/t12281493748ziy0hhc25o3odx.htm/, Retrieved Sun, 05 May 2024 09:45:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26976, Retrieved Sun, 05 May 2024 09:45:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact229

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] [2008-12-01 16:35:41] [59094f58b9d90d3694e930ebd2901ecd] [Current]
Feedback Forum
2008-12-04 18:20:08 [c97d2ae59c98cf77a04815c1edffab5a] [reply] 
het antwoord van de student is correct.
in de VRM wordt telkens de variantie berekend, nadat de tijdsreeks gedifferentieerd is met bepaalde waarden van d en D. wanneer d=0 en D=0 wordt de variantie van de ruwe gegevens/oorspronkelijke tijdsreeks berekend. het klopt inderdaad dat we naar de kleinste variantie moeten zoeken om zo te bepalen welke transformaties we moeten doorvoeren. aangezien de variantie gevoelig is voor outliers en zo de variantie vertekend kan zijn, gebruiken we best de getrimde variantie die de extreme waarden buiten beschouwing laat.

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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=26976&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=26976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26976&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)243.021547094188Range52Trim Var.198.857803437731
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.78224183812553Range8Trim Var.2.66246719160105
V(Y[t],d=0,D=1)12.4386676540883Range16Trim Var.7.17651852917206
V(Y[t],d=1,D=1)1.94231923002172Range4Trim Var.0
V(Y[t],d=2,D=1)3.90101395782954Range8Trim Var.2.22427460940506
V(Y[t],d=3,D=1)11.4793218028457Range16Trim Var.6.43898540163144
V(Y[t],d=0,D=2)18.1725608137992Range24Trim Var.8.6000052194791
V(Y[t],d=1,D=2)5.86496113701976Range8Trim Var.2.50180971264910
V(Y[t],d=2,D=2)11.8308489665569Range16Trim Var.6.14447552624584
V(Y[t],d=3,D=2)34.5593220338983Range32Trim Var.19.9075989484805

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 243.021547094188 & Range & 52 & Trim Var. & 198.857803437731 \tabularnewline
V(Y[t],d=1,D=0) & 1.00084506362122 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.95571824521426 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.78224183812553 & Range & 8 & Trim Var. & 2.66246719160105 \tabularnewline
V(Y[t],d=0,D=1) & 12.4386676540883 & Range & 16 & Trim Var. & 7.17651852917206 \tabularnewline
V(Y[t],d=1,D=1) & 1.94231923002172 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.90101395782954 & Range & 8 & Trim Var. & 2.22427460940506 \tabularnewline
V(Y[t],d=3,D=1) & 11.4793218028457 & Range & 16 & Trim Var. & 6.43898540163144 \tabularnewline
V(Y[t],d=0,D=2) & 18.1725608137992 & Range & 24 & Trim Var. & 8.6000052194791 \tabularnewline
V(Y[t],d=1,D=2) & 5.86496113701976 & Range & 8 & Trim Var. & 2.50180971264910 \tabularnewline
V(Y[t],d=2,D=2) & 11.8308489665569 & Range & 16 & Trim Var. & 6.14447552624584 \tabularnewline
V(Y[t],d=3,D=2) & 34.5593220338983 & Range & 32 & Trim Var. & 19.9075989484805 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26976&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]243.021547094188[/C][C]Range[/C][C]52[/C][C]Trim Var.[/C][C]198.857803437731[/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]1.95571824521426[/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]5.78224183812553[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66246719160105[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.4386676540883[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.17651852917206[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.94231923002172[/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]3.90101395782954[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.22427460940506[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.4793218028457[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.43898540163144[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]18.1725608137992[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]8.6000052194791[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.86496113701976[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.50180971264910[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.8308489665569[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.14447552624584[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.5593220338983[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]19.9075989484805[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26976&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)243.021547094188Range52Trim Var.198.857803437731
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.78224183812553Range8Trim Var.2.66246719160105
V(Y[t],d=0,D=1)12.4386676540883Range16Trim Var.7.17651852917206
V(Y[t],d=1,D=1)1.94231923002172Range4Trim Var.0
V(Y[t],d=2,D=1)3.90101395782954Range8Trim Var.2.22427460940506
V(Y[t],d=3,D=1)11.4793218028457Range16Trim Var.6.43898540163144
V(Y[t],d=0,D=2)18.1725608137992Range24Trim Var.8.6000052194791
V(Y[t],d=1,D=2)5.86496113701976Range8Trim Var.2.50180971264910
V(Y[t],d=2,D=2)11.8308489665569Range16Trim Var.6.14447552624584
V(Y[t],d=3,D=2)34.5593220338983Range32Trim Var.19.9075989484805


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')