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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 07:50:06 -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/t1228056671h9rqbjwtb670peh.htm/, Retrieved Sun, 19 May 2024 03:42:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26539, Retrieved Sun, 19 May 2024 03:42:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158

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]
- R       [Law of Averages] [] [2008-11-30 14:50:06] [28deb8481dba3cc87d2d53a86e0e0d0b] [Current]
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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 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=26539&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=26539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26539&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)107.057458917836Range35Trim Var.92.460418735767
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02816901408451Range4Trim Var.0
V(Y[t],d=3,D=0)6.01606412669566Range8Trim Var.2.75376827094474
V(Y[t],d=0,D=1)10.6234220890699Range18Trim Var.4.479614893408
V(Y[t],d=1,D=1)1.90946502057613Range4Trim Var.0
V(Y[t],d=2,D=1)4.15663315090577Range8Trim Var.2.12225132413713
V(Y[t],d=3,D=1)12.7438016528926Range16Trim Var.5.90940610375058
V(Y[t],d=0,D=2)20.8231225121628Range26Trim Var.12.3402919369787
V(Y[t],d=1,D=2)5.49365312014213Range8Trim Var.2.54027828367451
V(Y[t],d=2,D=2)12.2283298097252Range16Trim Var.6.40712333597814
V(Y[t],d=3,D=2)37.9993550005375Range32Trim Var.20.8976621140969

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 107.057458917836 & Range & 35 & Trim Var. & 92.460418735767 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.02816901408451 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.01606412669566 & Range & 8 & Trim Var. & 2.75376827094474 \tabularnewline
V(Y[t],d=0,D=1) & 10.6234220890699 & Range & 18 & Trim Var. & 4.479614893408 \tabularnewline
V(Y[t],d=1,D=1) & 1.90946502057613 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.15663315090577 & Range & 8 & Trim Var. & 2.12225132413713 \tabularnewline
V(Y[t],d=3,D=1) & 12.7438016528926 & Range & 16 & Trim Var. & 5.90940610375058 \tabularnewline
V(Y[t],d=0,D=2) & 20.8231225121628 & Range & 26 & Trim Var. & 12.3402919369787 \tabularnewline
V(Y[t],d=1,D=2) & 5.49365312014213 & Range & 8 & Trim Var. & 2.54027828367451 \tabularnewline
V(Y[t],d=2,D=2) & 12.2283298097252 & Range & 16 & Trim Var. & 6.40712333597814 \tabularnewline
V(Y[t],d=3,D=2) & 37.9993550005375 & Range & 32 & Trim Var. & 20.8976621140969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26539&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]107.057458917836[/C][C]Range[/C][C]35[/C][C]Trim Var.[/C][C]92.460418735767[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00132795711906[/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]2.02816901408451[/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]6.01606412669566[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.75376827094474[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.6234220890699[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.479614893408[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.90946502057613[/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]4.15663315090577[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.12225132413713[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.7438016528926[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.90940610375058[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.8231225121628[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]12.3402919369787[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.49365312014213[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.54027828367451[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.2283298097252[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.40712333597814[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.9993550005375[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.8976621140969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26539&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)107.057458917836Range35Trim Var.92.460418735767
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02816901408451Range4Trim Var.0
V(Y[t],d=3,D=0)6.01606412669566Range8Trim Var.2.75376827094474
V(Y[t],d=0,D=1)10.6234220890699Range18Trim Var.4.479614893408
V(Y[t],d=1,D=1)1.90946502057613Range4Trim Var.0
V(Y[t],d=2,D=1)4.15663315090577Range8Trim Var.2.12225132413713
V(Y[t],d=3,D=1)12.7438016528926Range16Trim Var.5.90940610375058
V(Y[t],d=0,D=2)20.8231225121628Range26Trim Var.12.3402919369787
V(Y[t],d=1,D=2)5.49365312014213Range8Trim Var.2.54027828367451
V(Y[t],d=2,D=2)12.2283298097252Range16Trim Var.6.40712333597814
V(Y[t],d=3,D=2)37.9993550005375Range32Trim Var.20.8976621140969


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')