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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 13:46:37 -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/t1228164431yj2sacn4olf75f7.htm/, Retrieved Sun, 05 May 2024 20:25:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27383, Retrieved Sun, 05 May 2024 20:25:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ2
Estimated Impact192

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] [Q2] [2008-12-01 20:46:37] [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=27383&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=27383&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27383&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)60.1685611222445Range33Trim Var.40.5739490577759
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)2.09255533199195Range4Trim Var.0
V(Y[t],d=3,D=0)6.25799961056663Range8Trim Var.2.82952256841606
V(Y[t],d=0,D=1)13.2133167266974Range20Trim Var.6.42293038988784
V(Y[t],d=1,D=1)1.92592592592593Range4Trim Var.0
V(Y[t],d=2,D=1)4.13194179288108Range8Trim Var.2.12898517145505
V(Y[t],d=3,D=1)12.4710573400358Range16Trim Var.6.0444286925813
V(Y[t],d=0,D=2)20.8243962848297Range24Trim Var.11.8618473895582
V(Y[t],d=1,D=2)5.65372418387742Range8Trim Var.2.56426379220001
V(Y[t],d=2,D=2)12.3211924960527Range16Trim Var.6.29071515774594
V(Y[t],d=3,D=2)37.4659404450496Range30Trim Var.20.2379171141810

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 60.1685611222445 & Range & 33 & Trim Var. & 40.5739490577759 \tabularnewline
V(Y[t],d=1,D=0) & 1.00168207901747 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.09255533199195 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.25799961056663 & Range & 8 & Trim Var. & 2.82952256841606 \tabularnewline
V(Y[t],d=0,D=1) & 13.2133167266974 & Range & 20 & Trim Var. & 6.42293038988784 \tabularnewline
V(Y[t],d=1,D=1) & 1.92592592592593 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.13194179288108 & Range & 8 & Trim Var. & 2.12898517145505 \tabularnewline
V(Y[t],d=3,D=1) & 12.4710573400358 & Range & 16 & Trim Var. & 6.0444286925813 \tabularnewline
V(Y[t],d=0,D=2) & 20.8243962848297 & Range & 24 & Trim Var. & 11.8618473895582 \tabularnewline
V(Y[t],d=1,D=2) & 5.65372418387742 & Range & 8 & Trim Var. & 2.56426379220001 \tabularnewline
V(Y[t],d=2,D=2) & 12.3211924960527 & Range & 16 & Trim Var. & 6.29071515774594 \tabularnewline
V(Y[t],d=3,D=2) & 37.4659404450496 & Range & 30 & Trim Var. & 20.2379171141810 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27383&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]60.1685611222445[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]40.5739490577759[/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]2.09255533199195[/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]6.25799961056663[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.82952256841606[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.2133167266974[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.42293038988784[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.92592592592593[/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]2.12898517145505[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.4710573400358[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.0444286925813[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]20.8243962848297[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]11.8618473895582[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.65372418387742[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.56426379220001[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.3211924960527[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.29071515774594[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]37.4659404450496[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]20.2379171141810[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27383&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27383&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)60.1685611222445Range33Trim Var.40.5739490577759
V(Y[t],d=1,D=0)1.00168207901747Range2Trim Var.NA
V(Y[t],d=2,D=0)2.09255533199195Range4Trim Var.0
V(Y[t],d=3,D=0)6.25799961056663Range8Trim Var.2.82952256841606
V(Y[t],d=0,D=1)13.2133167266974Range20Trim Var.6.42293038988784
V(Y[t],d=1,D=1)1.92592592592593Range4Trim Var.0
V(Y[t],d=2,D=1)4.13194179288108Range8Trim Var.2.12898517145505
V(Y[t],d=3,D=1)12.4710573400358Range16Trim Var.6.0444286925813
V(Y[t],d=0,D=2)20.8243962848297Range24Trim Var.11.8618473895582
V(Y[t],d=1,D=2)5.65372418387742Range8Trim Var.2.56426379220001
V(Y[t],d=2,D=2)12.3211924960527Range16Trim Var.6.29071515774594
V(Y[t],d=3,D=2)37.4659404450496Range30Trim Var.20.2379171141810


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')