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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 computationThu, 27 Nov 2008 11:19:05 -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/27/t1227810018ju6fyxk88bbxqfv.htm/, Retrieved Sun, 19 May 2024 11:12:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25872, Retrieved Sun, 19 May 2024 11:12:46 +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]
-         [Law of Averages] [q3] [2008-11-27 18:19:05] [09074fbe368d26382bb94e5bb318a104] [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=25872&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=25872&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25872&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)17.476248496994Range19Trim Var.12.2049285566370
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)2.04426559356137Range4Trim Var.0
V(Y[t],d=3,D=0)6.17741935483871Range8Trim Var.2.71899064091932
V(Y[t],d=0,D=1)9.47810280405292Range16Trim Var.4.10291858678955
V(Y[t],d=1,D=1)1.93413947828732Range4Trim Var.0
V(Y[t],d=2,D=1)4.13194179288108Range8Trim Var.2.22781514428292
V(Y[t],d=3,D=1)12.7024622987135Range16Trim Var.6.25123096591269
V(Y[t],d=0,D=2)17.7928173374613Range26Trim Var.7.44414686031741
V(Y[t],d=1,D=2)5.52740839440373Range8Trim Var.2.72382174688057
V(Y[t],d=2,D=2)11.9321861535580Range16Trim Var.6.42746564942039
V(Y[t],d=3,D=2)36.5931486723761Range30Trim Var.20.6918163280348

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 17.476248496994 & Range & 19 & Trim Var. & 12.2049285566370 \tabularnewline
V(Y[t],d=1,D=0) & 1.00168207901747 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.04426559356137 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.17741935483871 & Range & 8 & Trim Var. & 2.71899064091932 \tabularnewline
V(Y[t],d=0,D=1) & 9.47810280405292 & Range & 16 & Trim Var. & 4.10291858678955 \tabularnewline
V(Y[t],d=1,D=1) & 1.93413947828732 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.13194179288108 & Range & 8 & Trim Var. & 2.22781514428292 \tabularnewline
V(Y[t],d=3,D=1) & 12.7024622987135 & Range & 16 & Trim Var. & 6.25123096591269 \tabularnewline
V(Y[t],d=0,D=2) & 17.7928173374613 & Range & 26 & Trim Var. & 7.44414686031741 \tabularnewline
V(Y[t],d=1,D=2) & 5.52740839440373 & Range & 8 & Trim Var. & 2.72382174688057 \tabularnewline
V(Y[t],d=2,D=2) & 11.9321861535580 & Range & 16 & Trim Var. & 6.42746564942039 \tabularnewline
V(Y[t],d=3,D=2) & 36.5931486723761 & Range & 30 & Trim Var. & 20.6918163280348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25872&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]17.476248496994[/C][C]Range[/C][C]19[/C][C]Trim Var.[/C][C]12.2049285566370[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00168207901747[/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]2.04426559356137[/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]6.17741935483871[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.71899064091932[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9.47810280405292[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]4.10291858678955[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.93413947828732[/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]4.13194179288108[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.22781514428292[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.7024622987135[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.25123096591269[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]17.7928173374613[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]7.44414686031741[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.52740839440373[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72382174688057[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.9321861535580[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.42746564942039[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.5931486723761[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]20.6918163280348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25872&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25872&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)17.476248496994Range19Trim Var.12.2049285566370
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)2.04426559356137Range4Trim Var.0
V(Y[t],d=3,D=0)6.17741935483871Range8Trim Var.2.71899064091932
V(Y[t],d=0,D=1)9.47810280405292Range16Trim Var.4.10291858678955
V(Y[t],d=1,D=1)1.93413947828732Range4Trim Var.0
V(Y[t],d=2,D=1)4.13194179288108Range8Trim Var.2.22781514428292
V(Y[t],d=3,D=1)12.7024622987135Range16Trim Var.6.25123096591269
V(Y[t],d=0,D=2)17.7928173374613Range26Trim Var.7.44414686031741
V(Y[t],d=1,D=2)5.52740839440373Range8Trim Var.2.72382174688057
V(Y[t],d=2,D=2)11.9321861535580Range16Trim Var.6.42746564942039
V(Y[t],d=3,D=2)36.5931486723761Range30Trim Var.20.6918163280348


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')