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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationSun, 06 Nov 2016 13:21:53 +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/2016/Nov/06/t14784385414wwfj2iqinq5hsy.htm/, Retrieved Sat, 04 May 2024 01:21:20 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 01:21:20 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432

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 Maurice George Kendall' @ kendall.wessa.net

\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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Maurice George Kendall' @ kendall.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)3799.61Range264Trim Var.2270.64
V(Y[t],d=1,D=0)1098.33Range130Trim Var.777.924
V(Y[t],d=2,D=0)1583.5Range144Trim Var.1122.75
V(Y[t],d=3,D=0)3840.51Range224Trim Var.2686.42
V(Y[t],d=0,D=1)215.87Range62Trim Var.132.551
V(Y[t],d=1,D=1)78.8876Range30Trim Var.56.6894
V(Y[t],d=2,D=1)177.497Range50Trim Var.128.898
V(Y[t],d=3,D=1)563.571Range88Trim Var.405.403
V(Y[t],d=0,D=2)180.242Range53Trim Var.100.877
V(Y[t],d=1,D=2)127.122Range43Trim Var.60.7619
V(Y[t],d=2,D=2)368.36Range72Trim Var.216.129
V(Y[t],d=3,D=2)1244.02Range134Trim Var.642.468

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 3799.61 & Range & 264 & Trim Var. & 2270.64 \tabularnewline
V(Y[t],d=1,D=0) & 1098.33 & Range & 130 & Trim Var. & 777.924 \tabularnewline
V(Y[t],d=2,D=0) & 1583.5 & Range & 144 & Trim Var. & 1122.75 \tabularnewline
V(Y[t],d=3,D=0) & 3840.51 & Range & 224 & Trim Var. & 2686.42 \tabularnewline
V(Y[t],d=0,D=1) & 215.87 & Range & 62 & Trim Var. & 132.551 \tabularnewline
V(Y[t],d=1,D=1) & 78.8876 & Range & 30 & Trim Var. & 56.6894 \tabularnewline
V(Y[t],d=2,D=1) & 177.497 & Range & 50 & Trim Var. & 128.898 \tabularnewline
V(Y[t],d=3,D=1) & 563.571 & Range & 88 & Trim Var. & 405.403 \tabularnewline
V(Y[t],d=0,D=2) & 180.242 & Range & 53 & Trim Var. & 100.877 \tabularnewline
V(Y[t],d=1,D=2) & 127.122 & Range & 43 & Trim Var. & 60.7619 \tabularnewline
V(Y[t],d=2,D=2) & 368.36 & Range & 72 & Trim Var. & 216.129 \tabularnewline
V(Y[t],d=3,D=2) & 1244.02 & Range & 134 & Trim Var. & 642.468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]3799.61[/C][C]Range[/C][C]264[/C][C]Trim Var.[/C][C]2270.64[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1098.33[/C][C]Range[/C][C]130[/C][C]Trim Var.[/C][C]777.924[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1583.5[/C][C]Range[/C][C]144[/C][C]Trim Var.[/C][C]1122.75[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3840.51[/C][C]Range[/C][C]224[/C][C]Trim Var.[/C][C]2686.42[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]215.87[/C][C]Range[/C][C]62[/C][C]Trim Var.[/C][C]132.551[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]78.8876[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]56.6894[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]177.497[/C][C]Range[/C][C]50[/C][C]Trim Var.[/C][C]128.898[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]563.571[/C][C]Range[/C][C]88[/C][C]Trim Var.[/C][C]405.403[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]180.242[/C][C]Range[/C][C]53[/C][C]Trim Var.[/C][C]100.877[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]127.122[/C][C]Range[/C][C]43[/C][C]Trim Var.[/C][C]60.7619[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]368.36[/C][C]Range[/C][C]72[/C][C]Trim Var.[/C][C]216.129[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1244.02[/C][C]Range[/C][C]134[/C][C]Trim Var.[/C][C]642.468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)3799.61Range264Trim Var.2270.64
V(Y[t],d=1,D=0)1098.33Range130Trim Var.777.924
V(Y[t],d=2,D=0)1583.5Range144Trim Var.1122.75
V(Y[t],d=3,D=0)3840.51Range224Trim Var.2686.42
V(Y[t],d=0,D=1)215.87Range62Trim Var.132.551
V(Y[t],d=1,D=1)78.8876Range30Trim Var.56.6894
V(Y[t],d=2,D=1)177.497Range50Trim Var.128.898
V(Y[t],d=3,D=1)563.571Range88Trim Var.405.403
V(Y[t],d=0,D=2)180.242Range53Trim Var.100.877
V(Y[t],d=1,D=2)127.122Range43Trim Var.60.7619
V(Y[t],d=2,D=2)368.36Range72Trim Var.216.129
V(Y[t],d=3,D=2)1244.02Range134Trim Var.642.468


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()