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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationSun, 26 Dec 2010 11:35:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t12933632354o6z1p94y7h5tnt.htm/, Retrieved Mon, 06 May 2024 18:21:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115537, Retrieved Mon, 06 May 2024 18:21:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD    [Variance Reduction Matrix] [variantie reducti...] [2010-12-26 11:35:40] [ea05999e24dc6223e14cc730e7a15b1e] [Current]
-    D      [Variance Reduction Matrix] [variantie reducti...] [2010-12-26 11:44:54] [d4d7f64064e581afd5f11cb27d8ab03c]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14450609152
15369578496
16440317952
17674829824
19782035456
21531359232
23118405632
24779487232
26495297536
29388689408
32676600000
35799700000
40077000000
45536800000
53409700000
59108700000
67180700000
72656600000
78026600000
83450800000
90756100000
95153800000
102966000000
109085000000
117854000000
125345000000
131200000000
136486000000
146033000000
158348000000
167909000000
175906000000
184714000000
190243000000
200495000000
207782000000
211399000000
221184000000
229572000000
238248000000
251741000000
258883000000
267652000000
274726000000
290825000000
302845000000
318193000000
334948000000
344676000000
337284000000

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115537&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115537&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115537&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)1.07615163920262e+22Range330225390848Trim Var.8.39060487578254e+21
V(Y[t],d=1,D=0)19412531922088640512Range2.4147e+10Trim Var.9594589797847416832
V(Y[t],d=2,D=0)15309010832072372224Range2.6145e+10Trim Var.4764463443113236480
V(Y[t],d=3,D=0)28264313135357829120Range2.3824e+10Trim Var.15731354474709303296
V(Y[t],d=0,D=1)6.99384011602343e+20Range107650609152Trim Var.4.63353669138423e+20
V(Y[t],d=1,D=1)20995321936455368704Range2.6645e+10Trim Var.7275027840857472000
V(Y[t],d=2,D=1)27191101952779231232Range3.1502e+10Trim Var.6955431375284558848
V(Y[t],d=3,D=1)44061214602087112704Range3.3697e+10Trim Var.21225070931052056576
V(Y[t],d=0,D=2)1.33846384238470e+20Range45785809152Trim Var.7.0147621256866e+19
V(Y[t],d=1,D=2)45125102144559169536Range3.0734e+10Trim Var.19276759821058473984
V(Y[t],d=2,D=2)72025844195531210752Range40640500000Trim Var.17147389064264017920
V(Y[t],d=3,D=2)1.27528362762383e+20Range55209200000Trim Var.4.0632941787623e+19

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.07615163920262e+22 & Range & 330225390848 & Trim Var. & 8.39060487578254e+21 \tabularnewline
V(Y[t],d=1,D=0) & 19412531922088640512 & Range & 2.4147e+10 & Trim Var. & 9594589797847416832 \tabularnewline
V(Y[t],d=2,D=0) & 15309010832072372224 & Range & 2.6145e+10 & Trim Var. & 4764463443113236480 \tabularnewline
V(Y[t],d=3,D=0) & 28264313135357829120 & Range & 2.3824e+10 & Trim Var. & 15731354474709303296 \tabularnewline
V(Y[t],d=0,D=1) & 6.99384011602343e+20 & Range & 107650609152 & Trim Var. & 4.63353669138423e+20 \tabularnewline
V(Y[t],d=1,D=1) & 20995321936455368704 & Range & 2.6645e+10 & Trim Var. & 7275027840857472000 \tabularnewline
V(Y[t],d=2,D=1) & 27191101952779231232 & Range & 3.1502e+10 & Trim Var. & 6955431375284558848 \tabularnewline
V(Y[t],d=3,D=1) & 44061214602087112704 & Range & 3.3697e+10 & Trim Var. & 21225070931052056576 \tabularnewline
V(Y[t],d=0,D=2) & 1.33846384238470e+20 & Range & 45785809152 & Trim Var. & 7.0147621256866e+19 \tabularnewline
V(Y[t],d=1,D=2) & 45125102144559169536 & Range & 3.0734e+10 & Trim Var. & 19276759821058473984 \tabularnewline
V(Y[t],d=2,D=2) & 72025844195531210752 & Range & 40640500000 & Trim Var. & 17147389064264017920 \tabularnewline
V(Y[t],d=3,D=2) & 1.27528362762383e+20 & Range & 55209200000 & Trim Var. & 4.0632941787623e+19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115537&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.07615163920262e+22[/C][C]Range[/C][C]330225390848[/C][C]Trim Var.[/C][C]8.39060487578254e+21[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]19412531922088640512[/C][C]Range[/C][C]2.4147e+10[/C][C]Trim Var.[/C][C]9594589797847416832[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]15309010832072372224[/C][C]Range[/C][C]2.6145e+10[/C][C]Trim Var.[/C][C]4764463443113236480[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]28264313135357829120[/C][C]Range[/C][C]2.3824e+10[/C][C]Trim Var.[/C][C]15731354474709303296[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]6.99384011602343e+20[/C][C]Range[/C][C]107650609152[/C][C]Trim Var.[/C][C]4.63353669138423e+20[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]20995321936455368704[/C][C]Range[/C][C]2.6645e+10[/C][C]Trim Var.[/C][C]7275027840857472000[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]27191101952779231232[/C][C]Range[/C][C]3.1502e+10[/C][C]Trim Var.[/C][C]6955431375284558848[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]44061214602087112704[/C][C]Range[/C][C]3.3697e+10[/C][C]Trim Var.[/C][C]21225070931052056576[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1.33846384238470e+20[/C][C]Range[/C][C]45785809152[/C][C]Trim Var.[/C][C]7.0147621256866e+19[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]45125102144559169536[/C][C]Range[/C][C]3.0734e+10[/C][C]Trim Var.[/C][C]19276759821058473984[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]72025844195531210752[/C][C]Range[/C][C]40640500000[/C][C]Trim Var.[/C][C]17147389064264017920[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1.27528362762383e+20[/C][C]Range[/C][C]55209200000[/C][C]Trim Var.[/C][C]4.0632941787623e+19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115537&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115537&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)1.07615163920262e+22Range330225390848Trim Var.8.39060487578254e+21
V(Y[t],d=1,D=0)19412531922088640512Range2.4147e+10Trim Var.9594589797847416832
V(Y[t],d=2,D=0)15309010832072372224Range2.6145e+10Trim Var.4764463443113236480
V(Y[t],d=3,D=0)28264313135357829120Range2.3824e+10Trim Var.15731354474709303296
V(Y[t],d=0,D=1)6.99384011602343e+20Range107650609152Trim Var.4.63353669138423e+20
V(Y[t],d=1,D=1)20995321936455368704Range2.6645e+10Trim Var.7275027840857472000
V(Y[t],d=2,D=1)27191101952779231232Range3.1502e+10Trim Var.6955431375284558848
V(Y[t],d=3,D=1)44061214602087112704Range3.3697e+10Trim Var.21225070931052056576
V(Y[t],d=0,D=2)1.33846384238470e+20Range45785809152Trim Var.7.0147621256866e+19
V(Y[t],d=1,D=2)45125102144559169536Range3.0734e+10Trim Var.19276759821058473984
V(Y[t],d=2,D=2)72025844195531210752Range40640500000Trim Var.17147389064264017920
V(Y[t],d=3,D=2)1.27528362762383e+20Range55209200000Trim Var.4.0632941787623e+19


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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(myx,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')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()