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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 09:38:43 -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/Nov/30/t1228063171arpkhxoqrm8eo4g.htm/, Retrieved Sun, 19 May 2024 10:06:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26612, Retrieved Sun, 19 May 2024 10:06:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordslaw of avarage
Estimated Impact163

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] [law of avarage q3] [2008-11-30 16:38:43] [f4b2017b314c03698059f43b95818e67] [Current]
Feedback Forum
2008-12-05 15:24:58 [Kristof Van Esbroeck] [reply] 
Student geeft korte interpreatie van grafiek, zonder analyse.

De VRM - Variance Reduction Matrix – toont da variatie en gerelateerde differentiatiewaarden.

We noteren bij de kleinste variatiewaarde het meest adequate stationaire karakter.

In de tabel lezen we voorts kleine d waarden en grote D waarden af. Wanneer d=0 noteren we het aantal keer dat we niet seizonaal differentieren. In geval van D=0 noteren we het aantal keer dat we wel seizonaal differentieren.

0.99814086003332 wordt gevonden bij d=1 en D=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 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=26612&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=26612&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26612&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)78.3673106212425Range40Trim Var.48.1566757769005
V(Y[t],d=1,D=0)0.99814086003332Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85913876835309Range4Trim Var.0
V(Y[t],d=3,D=0)5.4757902252223Range8Trim Var.2.50712592237406
V(Y[t],d=0,D=1)12.0849463089508Range16Trim Var.4.80330740892345
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)3.47214797844809Range8Trim Var.0.917884111117683
V(Y[t],d=3,D=1)9.73553719008265Range16Trim Var.4.32812609065907
V(Y[t],d=0,D=2)27.9702078726227Range28Trim Var.13.5073977371627
V(Y[t],d=1,D=2)5.98310459693538Range8Trim Var.2.73665209069264
V(Y[t],d=2,D=2)9.93655721180007Range16Trim Var.5.89815611625532
V(Y[t],d=3,D=2)27.1016232486473Range30Trim Var.13.7224951214589

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 78.3673106212425 & Range & 40 & Trim Var. & 48.1566757769005 \tabularnewline
V(Y[t],d=1,D=0) & 0.99814086003332 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.85913876835309 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.4757902252223 & Range & 8 & Trim Var. & 2.50712592237406 \tabularnewline
V(Y[t],d=0,D=1) & 12.0849463089508 & Range & 16 & Trim Var. & 4.80330740892345 \tabularnewline
V(Y[t],d=1,D=1) & 2.02462375677069 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.47214797844809 & Range & 8 & Trim Var. & 0.917884111117683 \tabularnewline
V(Y[t],d=3,D=1) & 9.73553719008265 & Range & 16 & Trim Var. & 4.32812609065907 \tabularnewline
V(Y[t],d=0,D=2) & 27.9702078726227 & Range & 28 & Trim Var. & 13.5073977371627 \tabularnewline
V(Y[t],d=1,D=2) & 5.98310459693538 & Range & 8 & Trim Var. & 2.73665209069264 \tabularnewline
V(Y[t],d=2,D=2) & 9.93655721180007 & Range & 16 & Trim Var. & 5.89815611625532 \tabularnewline
V(Y[t],d=3,D=2) & 27.1016232486473 & Range & 30 & Trim Var. & 13.7224951214589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26612&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]78.3673106212425[/C][C]Range[/C][C]40[/C][C]Trim Var.[/C][C]48.1566757769005[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99814086003332[/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]1.85913876835309[/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]5.4757902252223[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.50712592237406[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.0849463089508[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.80330740892345[/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]3.47214797844809[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.917884111117683[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]9.73553719008265[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.32812609065907[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]27.9702078726227[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]13.5073977371627[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.98310459693538[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.73665209069264[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]9.93655721180007[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.89815611625532[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]27.1016232486473[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]13.7224951214589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26612&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26612&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)78.3673106212425Range40Trim Var.48.1566757769005
V(Y[t],d=1,D=0)0.99814086003332Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85913876835309Range4Trim Var.0
V(Y[t],d=3,D=0)5.4757902252223Range8Trim Var.2.50712592237406
V(Y[t],d=0,D=1)12.0849463089508Range16Trim Var.4.80330740892345
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)3.47214797844809Range8Trim Var.0.917884111117683
V(Y[t],d=3,D=1)9.73553719008265Range16Trim Var.4.32812609065907
V(Y[t],d=0,D=2)27.9702078726227Range28Trim Var.13.5073977371627
V(Y[t],d=1,D=2)5.98310459693538Range8Trim Var.2.73665209069264
V(Y[t],d=2,D=2)9.93655721180007Range16Trim Var.5.89815611625532
V(Y[t],d=3,D=2)27.1016232486473Range30Trim Var.13.7224951214589


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')