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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 14:13:23 -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/t12278204312km1cbn5tjs5kpo.htm/, Retrieved Sun, 19 May 2024 09:21:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25913, Retrieved Sun, 19 May 2024 09:21:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact203

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 21:13:23] [fdd69703d301fae09456f660b2f52997] [Current]
F           [Law of Averages] [Q3] [2008-11-30 19:12:15] [005293453b571dbccb80b45226e44173]
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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=25913&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=25913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25913&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)16.4125691382766Range16Trim Var.10.6412333478987
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.10865191146881Range4Trim Var.0
V(Y[t],d=3,D=0)6.50804828973843Range8Trim Var.2.7002785072014
V(Y[t],d=0,D=1)13.1296832396405Range20Trim Var.6.80238745865094
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.41125386241665
V(Y[t],d=3,D=1)12.0991053932010Range16Trim Var.6.90003070890322
V(Y[t],d=0,D=2)25.3230782839452Range26Trim Var.13.7583120204604
V(Y[t],d=1,D=2)5.8733466577837Range8Trim Var.2.5920542786449
V(Y[t],d=2,D=2)12.0591252531200Range16Trim Var.7.00244480934136
V(Y[t],d=3,D=2)36.5676353603039Range32Trim Var.20.6604488778055

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 16.4125691382766 & Range & 16 & Trim Var. & 10.6412333478987 \tabularnewline
V(Y[t],d=1,D=0) & 1.00190742931646 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.10865191146881 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.50804828973843 & Range & 8 & Trim Var. & 2.7002785072014 \tabularnewline
V(Y[t],d=0,D=1) & 13.1296832396405 & Range & 20 & Trim Var. & 6.80238745865094 \tabularnewline
V(Y[t],d=1,D=1) & 1.95878013537151 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.98348818463366 & Range & 8 & Trim Var. & 2.41125386241665 \tabularnewline
V(Y[t],d=3,D=1) & 12.0991053932010 & Range & 16 & Trim Var. & 6.90003070890322 \tabularnewline
V(Y[t],d=0,D=2) & 25.3230782839452 & Range & 26 & Trim Var. & 13.7583120204604 \tabularnewline
V(Y[t],d=1,D=2) & 5.8733466577837 & Range & 8 & Trim Var. & 2.5920542786449 \tabularnewline
V(Y[t],d=2,D=2) & 12.0591252531200 & Range & 16 & Trim Var. & 7.00244480934136 \tabularnewline
V(Y[t],d=3,D=2) & 36.5676353603039 & Range & 32 & Trim Var. & 20.6604488778055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25913&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]16.4125691382766[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]10.6412333478987[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00190742931646[/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]2.10865191146881[/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]6.50804828973843[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.7002785072014[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.1296832396405[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.80238745865094[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95878013537151[/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]3.98348818463366[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.41125386241665[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.0991053932010[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.90003070890322[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.3230782839452[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]13.7583120204604[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.8733466577837[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.5920542786449[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.0591252531200[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.00244480934136[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.5676353603039[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.6604488778055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25913&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)16.4125691382766Range16Trim Var.10.6412333478987
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.10865191146881Range4Trim Var.0
V(Y[t],d=3,D=0)6.50804828973843Range8Trim Var.2.7002785072014
V(Y[t],d=0,D=1)13.1296832396405Range20Trim Var.6.80238745865094
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)3.98348818463366Range8Trim Var.2.41125386241665
V(Y[t],d=3,D=1)12.0991053932010Range16Trim Var.6.90003070890322
V(Y[t],d=0,D=2)25.3230782839452Range26Trim Var.13.7583120204604
V(Y[t],d=1,D=2)5.8733466577837Range8Trim Var.2.5920542786449
V(Y[t],d=2,D=2)12.0591252531200Range16Trim Var.7.00244480934136
V(Y[t],d=3,D=2)36.5676353603039Range32Trim Var.20.6604488778055


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')