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Author

*The author of this computation has been verified*

R Software Module

rwasp_rngnorm.wasp

Title produced by software

Random Number Generator - Normal Distribution

Date of computation

Tue, 06 Dec 2016 19:39:19 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/06/t14810495954naqax95fuk3ju2.htm/, Retrieved Sat, 04 May 2024 11:27:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297899, Retrieved Sat, 04 May 2024 11:27:57 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Random Number Generator - Normal Distribution] [Normal distributi...] [2016-12-06 18:39:19] [325a18647724c80085378f2a448a1737] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big 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=297899&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=297899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297899&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Parameter	Value	Standard Deviation
# simulated values	10000	-
true mean	2.55	-
true standard deviation	0.367	-
mean	2.55184909155857	0.00361980598287082
standard deviation	0.361980598287082	0.00255958935706759

\begin{tabular}{lllllllll}
\hline
Parameter & Value & Standard Deviation \tabularnewline
# simulated values & 10000 & - \tabularnewline
true mean & 2.55 & - \tabularnewline
true standard deviation & 0.367 & - \tabularnewline
mean & 2.55184909155857 & 0.00361980598287082 \tabularnewline
standard deviation & 0.361980598287082 & 0.00255958935706759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297899&T=1

[TABLE]
[ROW][C]Parameter[/C][C]Value[/C][C]Standard Deviation[/C][/ROW]
[ROW][C]# simulated values[/C][C]10000[/C][C]-[/C][/ROW]
[ROW][C]true mean[/C][C]2.55[/C][C]-[/C][/ROW]
[ROW][C]true standard deviation[/C][C]0.367[/C][C]-[/C][/ROW]
[ROW][C]mean[/C][C]2.55184909155857[/C][C]0.00361980598287082[/C][/ROW]
[ROW][C]standard deviation[/C][C]0.361980598287082[/C][C]0.00255958935706759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297899&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Parameter	Value	Standard Deviation
# simulated values	10000	-
true mean	2.55	-
true standard deviation	0.367	-
mean	2.55184909155857	0.00361980598287082
standard deviation	0.361980598287082	0.00255958935706759

Frequency Table (Histogram)
Bins	Midpoint	Abs. Frequency	Rel. Frequency	Cumul. Rel. Freq.	Density
[1.2,1.4[	1.3	9	9e-04	9e-04	0.0045
[1.4,1.6[	1.5	41	0.0041	0.005	0.0205
[1.6,1.8[	1.7	138	0.0138	0.0188	0.069
[1.8,2[	1.9	441	0.0441	0.0629	0.2205
[2,2.2[	2.1	999	0.0999	0.1628	0.4995
[2.2,2.4[	2.3	1764	0.1764	0.3392	0.882
[2.4,2.6[	2.5	2177	0.2177	0.5569	1.0885
[2.6,2.8[	2.7	1975	0.1975	0.7544	0.9875
[2.8,3[	2.9	1371	0.1371	0.8915	0.6855
[3,3.2[	3.1	713	0.0713	0.9628	0.3565
[3.2,3.4[	3.3	283	0.0283	0.9911	0.1415
[3.4,3.6[	3.5	70	0.007	0.9981	0.035
[3.6,3.8[	3.7	18	0.0018	0.9999	0.009
[3.8,4]	3.9	1	1e-04	1	5e-04

\begin{tabular}{lllllllll}
\hline
Frequency Table (Histogram) \tabularnewline
Bins & Midpoint & Abs. Frequency & Rel. Frequency & Cumul. Rel. Freq. & Density \tabularnewline
[1.2,1.4[ & 1.3 & 9 & 9e-04 & 9e-04 & 0.0045 \tabularnewline
[1.4,1.6[ & 1.5 & 41 & 0.0041 & 0.005 & 0.0205 \tabularnewline
[1.6,1.8[ & 1.7 & 138 & 0.0138 & 0.0188 & 0.069 \tabularnewline
[1.8,2[ & 1.9 & 441 & 0.0441 & 0.0629 & 0.2205 \tabularnewline
[2,2.2[ & 2.1 & 999 & 0.0999 & 0.1628 & 0.4995 \tabularnewline
[2.2,2.4[ & 2.3 & 1764 & 0.1764 & 0.3392 & 0.882 \tabularnewline
[2.4,2.6[ & 2.5 & 2177 & 0.2177 & 0.5569 & 1.0885 \tabularnewline
[2.6,2.8[ & 2.7 & 1975 & 0.1975 & 0.7544 & 0.9875 \tabularnewline
[2.8,3[ & 2.9 & 1371 & 0.1371 & 0.8915 & 0.6855 \tabularnewline
[3,3.2[ & 3.1 & 713 & 0.0713 & 0.9628 & 0.3565 \tabularnewline
[3.2,3.4[ & 3.3 & 283 & 0.0283 & 0.9911 & 0.1415 \tabularnewline
[3.4,3.6[ & 3.5 & 70 & 0.007 & 0.9981 & 0.035 \tabularnewline
[3.6,3.8[ & 3.7 & 18 & 0.0018 & 0.9999 & 0.009 \tabularnewline
[3.8,4] & 3.9 & 1 & 1e-04 & 1 & 5e-04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297899&T=2

[TABLE]
[ROW][C]Frequency Table (Histogram)[/C][/ROW]
[ROW][C]Bins[/C][C]Midpoint[/C][C]Abs. Frequency[/C][C]Rel. Frequency[/C][C]Cumul. Rel. Freq.[/C][C]Density[/C][/ROW]
[ROW][C][1.2,1.4[[/C][C]1.3[/C][C]9[/C][C]9e-04[/C][C]9e-04[/C][C]0.0045[/C][/ROW]
[ROW][C][1.4,1.6[[/C][C]1.5[/C][C]41[/C][C]0.0041[/C][C]0.005[/C][C]0.0205[/C][/ROW]
[ROW][C][1.6,1.8[[/C][C]1.7[/C][C]138[/C][C]0.0138[/C][C]0.0188[/C][C]0.069[/C][/ROW]
[ROW][C][1.8,2[[/C][C]1.9[/C][C]441[/C][C]0.0441[/C][C]0.0629[/C][C]0.2205[/C][/ROW]
[ROW][C][2,2.2[[/C][C]2.1[/C][C]999[/C][C]0.0999[/C][C]0.1628[/C][C]0.4995[/C][/ROW]
[ROW][C][2.2,2.4[[/C][C]2.3[/C][C]1764[/C][C]0.1764[/C][C]0.3392[/C][C]0.882[/C][/ROW]
[ROW][C][2.4,2.6[[/C][C]2.5[/C][C]2177[/C][C]0.2177[/C][C]0.5569[/C][C]1.0885[/C][/ROW]
[ROW][C][2.6,2.8[[/C][C]2.7[/C][C]1975[/C][C]0.1975[/C][C]0.7544[/C][C]0.9875[/C][/ROW]
[ROW][C][2.8,3[[/C][C]2.9[/C][C]1371[/C][C]0.1371[/C][C]0.8915[/C][C]0.6855[/C][/ROW]
[ROW][C][3,3.2[[/C][C]3.1[/C][C]713[/C][C]0.0713[/C][C]0.9628[/C][C]0.3565[/C][/ROW]
[ROW][C][3.2,3.4[[/C][C]3.3[/C][C]283[/C][C]0.0283[/C][C]0.9911[/C][C]0.1415[/C][/ROW]
[ROW][C][3.4,3.6[[/C][C]3.5[/C][C]70[/C][C]0.007[/C][C]0.9981[/C][C]0.035[/C][/ROW]
[ROW][C][3.6,3.8[[/C][C]3.7[/C][C]18[/C][C]0.0018[/C][C]0.9999[/C][C]0.009[/C][/ROW]
[ROW][C][3.8,4][/C][C]3.9[/C][C]1[/C][C]1e-04[/C][C]1[/C][C]5e-04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297899&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Frequency Table (Histogram)
Bins	Midpoint	Abs. Frequency	Rel. Frequency	Cumul. Rel. Freq.	Density
[1.2,1.4[	1.3	9	9e-04	9e-04	0.0045
[1.4,1.6[	1.5	41	0.0041	0.005	0.0205
[1.6,1.8[	1.7	138	0.0138	0.0188	0.069
[1.8,2[	1.9	441	0.0441	0.0629	0.2205
[2,2.2[	2.1	999	0.0999	0.1628	0.4995
[2.2,2.4[	2.3	1764	0.1764	0.3392	0.882
[2.4,2.6[	2.5	2177	0.2177	0.5569	1.0885
[2.6,2.8[	2.7	1975	0.1975	0.7544	0.9875
[2.8,3[	2.9	1371	0.1371	0.8915	0.6855
[3,3.2[	3.1	713	0.0713	0.9628	0.3565
[3.2,3.4[	3.3	283	0.0283	0.9911	0.1415
[3.4,3.6[	3.5	70	0.007	0.9981	0.035
[3.6,3.8[	3.7	18	0.0018	0.9999	0.009
[3.8,4]	3.9	1	1e-04	1	5e-04

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 10000 ; par2 = 2.55 ; par3 = 0.367 ; par4 = 2 ; par5 = N ; par6 = 0 ;

Parameters (R input):

par1 = 10000 ; par2 = 2.55 ; par3 = 0.367 ; par4 = 2 ; par5 = N ; par6 = 0 ; par7 = ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- ''
par6 <- '0'
par5 <- 'N'
par4 <- '2'
par3 <- '0.367'
par2 <- '2.55'
par1 <- '100'
library(MASS)
library(msm)
par1 <- sub(',','.',par1)
par2 <- sub(',','.',par2)
par3 <- sub(',','.',par3)
par4 <- sub(',','.',par4)
par1 <- as.numeric(par1)
if (par1 > 10000) par1=10000 #impose restriction on number of random values
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
if (par6 == '0') par6 = 'Sturges' else {
par6 <- as.numeric(par6)
if (par6 > 50) par6 = 50 #impose restriction on the number of bins
}
if (par7 == '') par7 <- -Inf else par7 <- as.numeric(par7)
if (par8 == '') par8 <- Inf else par8 <- as.numeric(par8)
x <- rtnorm(par1,par2,par3,par7,par8)
x <- as.ts(x) #otherwise the fitdistr function does not work properly
if ((par7 == -Inf) & (par8 == Inf)) (r <- fitdistr(x,'normal'))
bitmap(file='test1.png')
myhist<-hist(x,col=par4,breaks=par6,main=main,ylab=ylab,xlab=xlab,freq=F)
if ((par7 == -Inf) & (par8 == Inf)) {
curve(1/(r$estimate[2]*sqrt(2*pi))*exp(-1/2*((x-r$estimate[1])/r$estimate[2])^2),min(x),max(x),add=T)
}
dev.off()
load(file='createtable')
if (par5 == 'Y')
{
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Index',1,TRUE)
a<-table.element(a,'Value',1,TRUE)
a<-table.row.end(a)
for (i in 1:par1)
{
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}
if ((par7 == -Inf) & (par8 == Inf)) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Parameter',1,TRUE)
a<-table.element(a,'Value',1,TRUE)
a<-table.element(a,'Standard Deviation',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'# simulated values',header=TRUE)
a<-table.element(a,par1)
a<-table.element(a,'-')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'true mean',header=TRUE)
a<-table.element(a,par2)
a<-table.element(a,'-')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'true standard deviation',header=TRUE)
a<-table.element(a,par3)
a<-table.element(a,'-')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'mean',header=TRUE)
a<-table.element(a,r$estimate[1])
a<-table.element(a,r$sd[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'standard deviation',header=TRUE)
a<-table.element(a,r$estimate[2])
a<-table.element(a,r$sd[2])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Frequency Table (Histogram)',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bins',header=TRUE)
a<-table.element(a,'Midpoint',header=TRUE)
a<-table.element(a,'Abs. Frequency',header=TRUE)
a<-table.element(a,'Rel. Frequency',header=TRUE)
a<-table.element(a,'Cumul. Rel. Freq.',header=TRUE)
a<-table.element(a,'Density',header=TRUE)
a<-table.row.end(a)
crf <- 0
mynumrows <- (length(myhist$breaks)-1)
for (i in 1:mynumrows) {
a<-table.row.start(a)
dum <- paste('[',myhist$breaks[i],sep='')
dum <- paste(dum,myhist$breaks[i+1],sep=',')
if (i==mynumrows)
dum <- paste(dum,']',sep='')
else
dum <- paste(dum,'[',sep='')
a<-table.element(a,dum,header=TRUE)
a<-table.element(a,myhist$mids[i])
a<-table.element(a,myhist$counts[i])
rf <- myhist$counts[i]/par1
crf <- crf + rf
a<-table.element(a,round(rf,6))
a<-table.element(a,round(crf,6))
a<-table.element(a,round(myhist$density[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable3.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code