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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 computationWed, 03 Dec 2008 04:11:45 -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/03/t1228302736fe2lg2qhz05o28e.htm/, Retrieved Fri, 17 May 2024 14:18:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28614, Retrieved Fri, 17 May 2024 14:18:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181

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] [Q3] [2008-12-02 20:13:15] [17bd4671b42d569d890f7246b2ee4ecc]
-           [Law of Averages] [] [2008-12-03 11:11:45] [d41d8cd98f00b204e9800998ecf8427e] [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 time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28614&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]0 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=28614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28614&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)16.9362885771543Range21Trim Var.10.1696679366312
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.92352508626054Range4Trim Var.0
V(Y[t],d=3,D=0)5.67741935483871Range8Trim Var.2.59642119940399
V(Y[t],d=0,D=1)12.1537516410274Range20Trim Var.6.59599000847495
V(Y[t],d=1,D=1)2.00796004765888Range4Trim Var.0
V(Y[t],d=2,D=1)3.81030927835052Range8Trim Var.2.37779543408019
V(Y[t],d=3,D=1)11.148743290449Range16Trim Var.7.10778331189322
V(Y[t],d=0,D=2)24.0150729765590Range28Trim Var.11.6895824344408
V(Y[t],d=1,D=2)6.0335953808572Range8Trim Var.2.68381072954581
V(Y[t],d=2,D=2)11.5855523144307Range16Trim Var.6.50374064837905
V(Y[t],d=3,D=2)33.9066184111513Range30Trim Var.22.3129439032506

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 16.9362885771543 & Range & 21 & Trim Var. & 10.1696679366312 \tabularnewline
V(Y[t],d=1,D=0) & 1.00197181511618 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.92352508626054 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.67741935483871 & Range & 8 & Trim Var. & 2.59642119940399 \tabularnewline
V(Y[t],d=0,D=1) & 12.1537516410274 & Range & 20 & Trim Var. & 6.59599000847495 \tabularnewline
V(Y[t],d=1,D=1) & 2.00796004765888 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.81030927835052 & Range & 8 & Trim Var. & 2.37779543408019 \tabularnewline
V(Y[t],d=3,D=1) & 11.148743290449 & Range & 16 & Trim Var. & 7.10778331189322 \tabularnewline
V(Y[t],d=0,D=2) & 24.0150729765590 & Range & 28 & Trim Var. & 11.6895824344408 \tabularnewline
V(Y[t],d=1,D=2) & 6.0335953808572 & Range & 8 & Trim Var. & 2.68381072954581 \tabularnewline
V(Y[t],d=2,D=2) & 11.5855523144307 & Range & 16 & Trim Var. & 6.50374064837905 \tabularnewline
V(Y[t],d=3,D=2) & 33.9066184111513 & Range & 30 & Trim Var. & 22.3129439032506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28614&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]16.9362885771543[/C][C]Range[/C][C]21[/C][C]Trim Var.[/C][C]10.1696679366312[/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]1.92352508626054[/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]5.67741935483871[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59642119940399[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.1537516410274[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.59599000847495[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.00796004765888[/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]3.81030927835052[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.37779543408019[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.148743290449[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.10778331189322[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.0150729765590[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]11.6895824344408[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.0335953808572[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.68381072954581[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.5855523144307[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.50374064837905[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]33.9066184111513[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]22.3129439032506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28614&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)16.9362885771543Range21Trim Var.10.1696679366312
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.92352508626054Range4Trim Var.0
V(Y[t],d=3,D=0)5.67741935483871Range8Trim Var.2.59642119940399
V(Y[t],d=0,D=1)12.1537516410274Range20Trim Var.6.59599000847495
V(Y[t],d=1,D=1)2.00796004765888Range4Trim Var.0
V(Y[t],d=2,D=1)3.81030927835052Range8Trim Var.2.37779543408019
V(Y[t],d=3,D=1)11.148743290449Range16Trim Var.7.10778331189322
V(Y[t],d=0,D=2)24.0150729765590Range28Trim Var.11.6895824344408
V(Y[t],d=1,D=2)6.0335953808572Range8Trim Var.2.68381072954581
V(Y[t],d=2,D=2)11.5855523144307Range16Trim Var.6.50374064837905
V(Y[t],d=3,D=2)33.9066184111513Range30Trim Var.22.3129439032506


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')