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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 13:50:15 -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/t122816464794gmnt5r0iw1nm3.htm/, Retrieved Sun, 05 May 2024 14:39:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27388, Retrieved Sun, 05 May 2024 14:39:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ3
Estimated Impact201

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] [2008-11-29 12:49:16] [6743688719638b0cb1c0a6e0bf433315]
F         [Law of Averages] [q3] [2008-12-01 18:47:27] [988ab43f527fc78aae41c84649095267]
-             [Law of Averages] [Q3] [2008-12-01 20:50:15] [783db4b4a0f63b73ca8b14666b7f4329] [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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27388&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27388&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27388&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)65.5525611222445Range36Trim Var.42.2770978103416
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06036217303823Range4Trim Var.0
V(Y[t],d=3,D=0)6.29837087038359Range8Trim Var.2.66959489447667
V(Y[t],d=0,D=1)11.6152421988084Range16Trim Var.6.30757231825854
V(Y[t],d=1,D=1)2.12345679012346Range4Trim Var.0
V(Y[t],d=2,D=1)4.52781808154088Range8Trim Var.2.42905465551006
V(Y[t],d=3,D=1)14.1238135809832Range16Trim Var.6.5348226902631
V(Y[t],d=0,D=2)23.3001857585139Range28Trim Var.11.5709081226323
V(Y[t],d=1,D=2)6.38802576060404Range8Trim Var.2.83233662607653
V(Y[t],d=2,D=2)13.6489772615766Range16Trim Var.7.31069578333005
V(Y[t],d=3,D=2)42.677894435088Range32Trim Var.22.8842580510465

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 65.5525611222445 & Range & 36 & Trim Var. & 42.2770978103416 \tabularnewline
V(Y[t],d=1,D=0) & 1.00197181511618 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.06036217303823 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.29837087038359 & Range & 8 & Trim Var. & 2.66959489447667 \tabularnewline
V(Y[t],d=0,D=1) & 11.6152421988084 & Range & 16 & Trim Var. & 6.30757231825854 \tabularnewline
V(Y[t],d=1,D=1) & 2.12345679012346 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.52781808154088 & Range & 8 & Trim Var. & 2.42905465551006 \tabularnewline
V(Y[t],d=3,D=1) & 14.1238135809832 & Range & 16 & Trim Var. & 6.5348226902631 \tabularnewline
V(Y[t],d=0,D=2) & 23.3001857585139 & Range & 28 & Trim Var. & 11.5709081226323 \tabularnewline
V(Y[t],d=1,D=2) & 6.38802576060404 & Range & 8 & Trim Var. & 2.83233662607653 \tabularnewline
V(Y[t],d=2,D=2) & 13.6489772615766 & Range & 16 & Trim Var. & 7.31069578333005 \tabularnewline
V(Y[t],d=3,D=2) & 42.677894435088 & Range & 32 & Trim Var. & 22.8842580510465 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27388&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]65.5525611222445[/C][C]Range[/C][C]36[/C][C]Trim Var.[/C][C]42.2770978103416[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00197181511618[/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]2.06036217303823[/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]6.29837087038359[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66959489447667[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.6152421988084[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.30757231825854[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.12345679012346[/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]4.52781808154088[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.42905465551006[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]14.1238135809832[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.5348226902631[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.3001857585139[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]11.5709081226323[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.38802576060404[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.83233662607653[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.6489772615766[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.31069578333005[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]42.677894435088[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.8842580510465[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27388&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27388&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)65.5525611222445Range36Trim Var.42.2770978103416
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06036217303823Range4Trim Var.0
V(Y[t],d=3,D=0)6.29837087038359Range8Trim Var.2.66959489447667
V(Y[t],d=0,D=1)11.6152421988084Range16Trim Var.6.30757231825854
V(Y[t],d=1,D=1)2.12345679012346Range4Trim Var.0
V(Y[t],d=2,D=1)4.52781808154088Range8Trim Var.2.42905465551006
V(Y[t],d=3,D=1)14.1238135809832Range16Trim Var.6.5348226902631
V(Y[t],d=0,D=2)23.3001857585139Range28Trim Var.11.5709081226323
V(Y[t],d=1,D=2)6.38802576060404Range8Trim Var.2.83233662607653
V(Y[t],d=2,D=2)13.6489772615766Range16Trim Var.7.31069578333005
V(Y[t],d=3,D=2)42.677894435088Range32Trim Var.22.8842580510465


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')