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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationTue, 02 Dec 2008 13:15:47 -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/02/t1228249019k4wwu1eg7mcdnuv.htm/, Retrieved Sun, 19 May 2024 00:53:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28350, Retrieved Sun, 19 May 2024 00:53:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

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] [Non stationary ti...] [2008-12-02 20:15:47] [74a138e5b32af267311b5ad4cd13bf7e] [Current]
-           [Law of Averages] [Non stationary ti...] [2008-12-02 20:17:35] [1a689e9ccc515e1757f0522229a687e9]
-             [Law of Averages] [Non stationary ti...] [2008-12-02 20:18:57] [1a689e9ccc515e1757f0522229a687e9]
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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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28350&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28350&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)25.7160881763527Range26Trim Var.15.126390498851
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.05229772207542Range4Trim Var.0
V(Y[t],d=3,D=0)6.09677419354839Range8Trim Var.2.77909423736631
V(Y[t],d=0,D=1)12.805534049214Range20Trim Var.6.24723141090177
V(Y[t],d=1,D=1)2.07380366905806Range4Trim Var.0
V(Y[t],d=2,D=1)4.18142632896356Range8Trim Var.2.44897185423079
V(Y[t],d=3,D=1)12.4709210189997Range16Trim Var.6.97709206532736
V(Y[t],d=0,D=2)29.0609111012826Range30Trim Var.15.6581498650464
V(Y[t],d=1,D=2)6.27819675771708Range8Trim Var.2.68154786693542
V(Y[t],d=2,D=2)12.3298097251586Range16Trim Var.7.38288633461047
V(Y[t],d=3,D=2)36.4406062994948Range28Trim Var.23.9692075996293

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 25.7160881763527 & Range & 26 & Trim Var. & 15.126390498851 \tabularnewline
V(Y[t],d=1,D=0) & 1.00152111451819 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.05229772207542 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.09677419354839 & Range & 8 & Trim Var. & 2.77909423736631 \tabularnewline
V(Y[t],d=0,D=1) & 12.805534049214 & Range & 20 & Trim Var. & 6.24723141090177 \tabularnewline
V(Y[t],d=1,D=1) & 2.07380366905806 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.18142632896356 & Range & 8 & Trim Var. & 2.44897185423079 \tabularnewline
V(Y[t],d=3,D=1) & 12.4709210189997 & Range & 16 & Trim Var. & 6.97709206532736 \tabularnewline
V(Y[t],d=0,D=2) & 29.0609111012826 & Range & 30 & Trim Var. & 15.6581498650464 \tabularnewline
V(Y[t],d=1,D=2) & 6.27819675771708 & Range & 8 & Trim Var. & 2.68154786693542 \tabularnewline
V(Y[t],d=2,D=2) & 12.3298097251586 & Range & 16 & Trim Var. & 7.38288633461047 \tabularnewline
V(Y[t],d=3,D=2) & 36.4406062994948 & Range & 28 & Trim Var. & 23.9692075996293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28350&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]25.7160881763527[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]15.126390498851[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00152111451819[/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]2.05229772207542[/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]6.09677419354839[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.77909423736631[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.805534049214[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.24723141090177[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.07380366905806[/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]4.18142632896356[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.44897185423079[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.4709210189997[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.97709206532736[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]29.0609111012826[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]15.6581498650464[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.27819675771708[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.68154786693542[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.3298097251586[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.38288633461047[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.4406062994948[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]23.9692075996293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28350&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)25.7160881763527Range26Trim Var.15.126390498851
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.05229772207542Range4Trim Var.0
V(Y[t],d=3,D=0)6.09677419354839Range8Trim Var.2.77909423736631
V(Y[t],d=0,D=1)12.805534049214Range20Trim Var.6.24723141090177
V(Y[t],d=1,D=1)2.07380366905806Range4Trim Var.0
V(Y[t],d=2,D=1)4.18142632896356Range8Trim Var.2.44897185423079
V(Y[t],d=3,D=1)12.4709210189997Range16Trim Var.6.97709206532736
V(Y[t],d=0,D=2)29.0609111012826Range30Trim Var.15.6581498650464
V(Y[t],d=1,D=2)6.27819675771708Range8Trim Var.2.68154786693542
V(Y[t],d=2,D=2)12.3298097251586Range16Trim Var.7.38288633461047
V(Y[t],d=3,D=2)36.4406062994948Range28Trim Var.23.9692075996293


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')