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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 computationThu, 01 Feb 2018 09:19:10 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Feb/01/t15174731601vv7n18vzt0gbeg.htm/, Retrieved Mon, 29 Apr 2024 05:13:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=313428, Retrieved Mon, 29 Apr 2024 05:13:52 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact40

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [Vraag 4] [2018-02-01 08:19:10] [b4c215a57d838e3992780a1253393c3b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
15
14
14
8
19
17
18
10
15
16
12
13
10
14
15
20
9
12
13
16
12
14
15
19
16
16
14
14
14
13
18
15
15
15
13
14
15
14
19
16
16
12
10
11
13
14
11
11
16
9
16
19
13
15
14
15
11
14
15
17
16
13
15
14
15
14
12
12
15
17
13
5
7
10
15
9
9
15
14
11
18
20
20
16
15
14
13
18
14
12
9
19
13
12
14
6
14
11
11
14
12
19
13
14
17
12
16
15
15
15
16
15
12
13
14
17
14
14
14
15
11
11
16
12
12
19
18
16
16
13
11
10
14
14
14
16
10
16
7
16
15
17
11
11
10
13
14
13
13
12
10
15
6
15
15
11
14
14
16
12
15
20
12
9
13
15
19
11
11
17
15
14
15
11
12
15
16
16

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313428&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=313428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313428&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)8.21505Range15Trim Var.4.07893
V(Y[t],d=1,D=0)14.7785Range22Trim Var.8.30625
V(Y[t],d=2,D=0)42.7549Range34Trim Var.23.5974
V(Y[t],d=3,D=0)140.896Range63Trim Var.74.7885
V(Y[t],d=0,D=1)18.8548Range24Trim Var.10.3938
V(Y[t],d=1,D=1)30.5696Range35Trim Var.16.8802
V(Y[t],d=2,D=1)85.5596Range60Trim Var.49.8584
V(Y[t],d=3,D=1)275.222Range103Trim Var.160.719
V(Y[t],d=0,D=2)59.6897Range44Trim Var.30.9548
V(Y[t],d=1,D=2)89.1763Range55Trim Var.53.6439
V(Y[t],d=2,D=2)246.138Range91Trim Var.153.021
V(Y[t],d=3,D=2)779.579Range156Trim Var.480.454

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 8.21505 & Range & 15 & Trim Var. & 4.07893 \tabularnewline
V(Y[t],d=1,D=0) & 14.7785 & Range & 22 & Trim Var. & 8.30625 \tabularnewline
V(Y[t],d=2,D=0) & 42.7549 & Range & 34 & Trim Var. & 23.5974 \tabularnewline
V(Y[t],d=3,D=0) & 140.896 & Range & 63 & Trim Var. & 74.7885 \tabularnewline
V(Y[t],d=0,D=1) & 18.8548 & Range & 24 & Trim Var. & 10.3938 \tabularnewline
V(Y[t],d=1,D=1) & 30.5696 & Range & 35 & Trim Var. & 16.8802 \tabularnewline
V(Y[t],d=2,D=1) & 85.5596 & Range & 60 & Trim Var. & 49.8584 \tabularnewline
V(Y[t],d=3,D=1) & 275.222 & Range & 103 & Trim Var. & 160.719 \tabularnewline
V(Y[t],d=0,D=2) & 59.6897 & Range & 44 & Trim Var. & 30.9548 \tabularnewline
V(Y[t],d=1,D=2) & 89.1763 & Range & 55 & Trim Var. & 53.6439 \tabularnewline
V(Y[t],d=2,D=2) & 246.138 & Range & 91 & Trim Var. & 153.021 \tabularnewline
V(Y[t],d=3,D=2) & 779.579 & Range & 156 & Trim Var. & 480.454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313428&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]8.21505[/C][C]Range[/C][C]15[/C][C]Trim Var.[/C][C]4.07893[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]14.7785[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]8.30625[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]42.7549[/C][C]Range[/C][C]34[/C][C]Trim Var.[/C][C]23.5974[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]140.896[/C][C]Range[/C][C]63[/C][C]Trim Var.[/C][C]74.7885[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]18.8548[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]10.3938[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]30.5696[/C][C]Range[/C][C]35[/C][C]Trim Var.[/C][C]16.8802[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]85.5596[/C][C]Range[/C][C]60[/C][C]Trim Var.[/C][C]49.8584[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]275.222[/C][C]Range[/C][C]103[/C][C]Trim Var.[/C][C]160.719[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]59.6897[/C][C]Range[/C][C]44[/C][C]Trim Var.[/C][C]30.9548[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]89.1763[/C][C]Range[/C][C]55[/C][C]Trim Var.[/C][C]53.6439[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]246.138[/C][C]Range[/C][C]91[/C][C]Trim Var.[/C][C]153.021[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]779.579[/C][C]Range[/C][C]156[/C][C]Trim Var.[/C][C]480.454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313428&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)8.21505Range15Trim Var.4.07893
V(Y[t],d=1,D=0)14.7785Range22Trim Var.8.30625
V(Y[t],d=2,D=0)42.7549Range34Trim Var.23.5974
V(Y[t],d=3,D=0)140.896Range63Trim Var.74.7885
V(Y[t],d=0,D=1)18.8548Range24Trim Var.10.3938
V(Y[t],d=1,D=1)30.5696Range35Trim Var.16.8802
V(Y[t],d=2,D=1)85.5596Range60Trim Var.49.8584
V(Y[t],d=3,D=1)275.222Range103Trim Var.160.719
V(Y[t],d=0,D=2)59.6897Range44Trim Var.30.9548
V(Y[t],d=1,D=2)89.1763Range55Trim Var.53.6439
V(Y[t],d=2,D=2)246.138Range91Trim Var.153.021
V(Y[t],d=3,D=2)779.579Range156Trim Var.480.454


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.orig <- length(x)
x <- na.omit(x)
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)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
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,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(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()