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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 computationSun, 30 Nov 2008 09:37:50 -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/30/t1228063099wb1qfvogmykkn47.htm/, Retrieved Sun, 26 May 2024 10:16:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26610, Retrieved Sun, 26 May 2024 10:16:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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 Non Stationary...] [2008-11-30 16:37:50] [5e9e099b83e50415d7642e10d74756e4] [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=26610&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=26610&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26610&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)27.1458917835671Range24Trim Var.17.0261463710902
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.17303822937626Range4Trim Var.0
V(Y[t],d=3,D=0)6.73385474135133Range8Trim Var.2.79043572769489
V(Y[t],d=0,D=1)10.2661157302993Range16Trim Var.3.85721985815603
V(Y[t],d=1,D=1)2.00823045267490Range4Trim Var.0
V(Y[t],d=2,D=1)4.15663315090577Range8Trim Var.2.33603134041044
V(Y[t],d=3,D=1)12.6198176706143Range16Trim Var.6.5087148589294
V(Y[t],d=0,D=2)19.5510482087572Range24Trim Var.11.5407243855658
V(Y[t],d=1,D=2)6.00836775483011Range8Trim Var.2.72588141401812
V(Y[t],d=2,D=2)12.1268498942918Range16Trim Var.6.778252163071
V(Y[t],d=3,D=2)36.4061346615544Range28Trim Var.22.6366478136593

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 27.1458917835671 & Range & 24 & Trim Var. & 17.0261463710902 \tabularnewline
V(Y[t],d=1,D=0) & 0.99987927662554 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.17303822937626 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.73385474135133 & Range & 8 & Trim Var. & 2.79043572769489 \tabularnewline
V(Y[t],d=0,D=1) & 10.2661157302993 & Range & 16 & Trim Var. & 3.85721985815603 \tabularnewline
V(Y[t],d=1,D=1) & 2.00823045267490 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.15663315090577 & Range & 8 & Trim Var. & 2.33603134041044 \tabularnewline
V(Y[t],d=3,D=1) & 12.6198176706143 & Range & 16 & Trim Var. & 6.5087148589294 \tabularnewline
V(Y[t],d=0,D=2) & 19.5510482087572 & Range & 24 & Trim Var. & 11.5407243855658 \tabularnewline
V(Y[t],d=1,D=2) & 6.00836775483011 & Range & 8 & Trim Var. & 2.72588141401812 \tabularnewline
V(Y[t],d=2,D=2) & 12.1268498942918 & Range & 16 & Trim Var. & 6.778252163071 \tabularnewline
V(Y[t],d=3,D=2) & 36.4061346615544 & Range & 28 & Trim Var. & 22.6366478136593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26610&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]27.1458917835671[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]17.0261463710902[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99987927662554[/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]2.17303822937626[/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]6.73385474135133[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.79043572769489[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.2661157302993[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]3.85721985815603[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.00823045267490[/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]4.15663315090577[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.33603134041044[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.6198176706143[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.5087148589294[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.5510482087572[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]11.5407243855658[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.00836775483011[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.72588141401812[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.1268498942918[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.778252163071[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.4061346615544[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]22.6366478136593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26610&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26610&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)27.1458917835671Range24Trim Var.17.0261463710902
V(Y[t],d=1,D=0)0.99987927662554Range2Trim Var.NA
V(Y[t],d=2,D=0)2.17303822937626Range4Trim Var.0
V(Y[t],d=3,D=0)6.73385474135133Range8Trim Var.2.79043572769489
V(Y[t],d=0,D=1)10.2661157302993Range16Trim Var.3.85721985815603
V(Y[t],d=1,D=1)2.00823045267490Range4Trim Var.0
V(Y[t],d=2,D=1)4.15663315090577Range8Trim Var.2.33603134041044
V(Y[t],d=3,D=1)12.6198176706143Range16Trim Var.6.5087148589294
V(Y[t],d=0,D=2)19.5510482087572Range24Trim Var.11.5407243855658
V(Y[t],d=1,D=2)6.00836775483011Range8Trim Var.2.72588141401812
V(Y[t],d=2,D=2)12.1268498942918Range16Trim Var.6.778252163071
V(Y[t],d=3,D=2)36.4061346615544Range28Trim Var.22.6366478136593


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')