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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 11:43:46 -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/t1228157069ht305i829pxhgqk.htm/, Retrieved Sun, 05 May 2024 19:53:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27123, Retrieved Sun, 05 May 2024 19:53:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact224

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]
-           [Law of Averages] [q1] [2008-12-01 18:43:46] [5d823194959040fa9b19b8c8302177e6] [Current]
-             [Law of Averages] [Q1] [2008-12-01 20:44:52] [fe7291e888d31b8c4db0b24d6c0f75c6]
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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=27123&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=27123&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27123&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)163.761026052104Range45Trim Var.125.358492114795
V(Y[t],d=1,D=0)0.996499022140667Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06839430155229Range4Trim Var.0
V(Y[t],d=3,D=0)6.34675796715779Range8Trim Var.2.62924791086351
V(Y[t],d=0,D=1)11.8850775911401Range18Trim Var.4.64290230317628
V(Y[t],d=1,D=1)1.97530864197531Range4Trim Var.0
V(Y[t],d=2,D=1)4.09072164948454Range8Trim Var.2.37726970033296
V(Y[t],d=3,D=1)12.5371730425151Range16Trim Var.7.06860348051201
V(Y[t],d=0,D=2)25.4439451570102Range28Trim Var.15.0778682440534
V(Y[t],d=1,D=2)5.91545192094159Range8Trim Var.2.6285927701094
V(Y[t],d=2,D=2)12.4226724114861Range16Trim Var.6.7734778515635
V(Y[t],d=3,D=2)38.2796431002974Range32Trim Var.23.2658525072318

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 163.761026052104 & Range & 45 & Trim Var. & 125.358492114795 \tabularnewline
V(Y[t],d=1,D=0) & 0.996499022140667 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.06839430155229 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.34675796715779 & Range & 8 & Trim Var. & 2.62924791086351 \tabularnewline
V(Y[t],d=0,D=1) & 11.8850775911401 & Range & 18 & Trim Var. & 4.64290230317628 \tabularnewline
V(Y[t],d=1,D=1) & 1.97530864197531 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.09072164948454 & Range & 8 & Trim Var. & 2.37726970033296 \tabularnewline
V(Y[t],d=3,D=1) & 12.5371730425151 & Range & 16 & Trim Var. & 7.06860348051201 \tabularnewline
V(Y[t],d=0,D=2) & 25.4439451570102 & Range & 28 & Trim Var. & 15.0778682440534 \tabularnewline
V(Y[t],d=1,D=2) & 5.91545192094159 & Range & 8 & Trim Var. & 2.6285927701094 \tabularnewline
V(Y[t],d=2,D=2) & 12.4226724114861 & Range & 16 & Trim Var. & 6.7734778515635 \tabularnewline
V(Y[t],d=3,D=2) & 38.2796431002974 & Range & 32 & Trim Var. & 23.2658525072318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27123&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]163.761026052104[/C][C]Range[/C][C]45[/C][C]Trim Var.[/C][C]125.358492114795[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.996499022140667[/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]2.06839430155229[/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]6.34675796715779[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.62924791086351[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.8850775911401[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.64290230317628[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.97530864197531[/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]4.09072164948454[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.37726970033296[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.5371730425151[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.06860348051201[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.4439451570102[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]15.0778682440534[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.91545192094159[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.6285927701094[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.4226724114861[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.7734778515635[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.2796431002974[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]23.2658525072318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27123&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27123&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)163.761026052104Range45Trim Var.125.358492114795
V(Y[t],d=1,D=0)0.996499022140667Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06839430155229Range4Trim Var.0
V(Y[t],d=3,D=0)6.34675796715779Range8Trim Var.2.62924791086351
V(Y[t],d=0,D=1)11.8850775911401Range18Trim Var.4.64290230317628
V(Y[t],d=1,D=1)1.97530864197531Range4Trim Var.0
V(Y[t],d=2,D=1)4.09072164948454Range8Trim Var.2.37726970033296
V(Y[t],d=3,D=1)12.5371730425151Range16Trim Var.7.06860348051201
V(Y[t],d=0,D=2)25.4439451570102Range28Trim Var.15.0778682440534
V(Y[t],d=1,D=2)5.91545192094159Range8Trim Var.2.6285927701094
V(Y[t],d=2,D=2)12.4226724114861Range16Trim Var.6.7734778515635
V(Y[t],d=3,D=2)38.2796431002974Range32Trim Var.23.2658525072318


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')