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Author's title

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

Wed, 05 Oct 2016 14:39:36 +0200

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/05/t1475671195ydj23dthporva5g.htm/, Retrieved Sun, 05 May 2024 10:41:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296560, Retrieved Sun, 05 May 2024 10:41:28 +0000

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-     [Binomial Probabilities] [bernoulli ] [2016-10-05 11:56:28] [2de65f32e81449e9ab36f33175b2d919]
- RMP     [Random Number Generator - Normal Distribution] [random number 100] [2016-10-05 12:39:36] [94ac3c9a028ddd47e8862e80eac9f626] [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	4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296560&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]

4 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=296560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296560&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	4 seconds
R Server	Big Analytics Cloud Computing Center

Parameter	Value	Standard Deviation
# simulated values	100	-
true mean	5	-
true standard deviation	2.5	-
mean	4.88901929636656	0.239404708447678
standard deviation	2.39404708447678	0.169284692791341

\begin{tabular}{lllllllll}
\hline
Parameter & Value & Standard Deviation \tabularnewline
# simulated values & 100 & - \tabularnewline
true mean & 5 & - \tabularnewline
true standard deviation & 2.5 & - \tabularnewline
mean & 4.88901929636656 & 0.239404708447678 \tabularnewline
standard deviation & 2.39404708447678 & 0.169284692791341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296560&T=1

[TABLE]
[ROW][C]Parameter[/C][C]Value[/C][C]Standard Deviation[/C][/ROW]
[ROW][C]# simulated values[/C][C]100[/C][C]-[/C][/ROW]
[ROW][C]true mean[/C][C]5[/C][C]-[/C][/ROW]
[ROW][C]true standard deviation[/C][C]2.5[/C][C]-[/C][/ROW]
[ROW][C]mean[/C][C]4.88901929636656[/C][C]0.239404708447678[/C][/ROW]
[ROW][C]standard deviation[/C][C]2.39404708447678[/C][C]0.169284692791341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296560&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	100	-
true mean	5	-
true standard deviation	2.5	-
mean	4.88901929636656	0.239404708447678
standard deviation	2.39404708447678	0.169284692791341

Frequency Table (Histogram)
Bins	Midpoint	Abs. Frequency	Rel. Frequency	Cumul. Rel. Freq.	Density
[-1,0[	-0.5	1	0.01	0.01	0.01
[0,1[	0.5	3	0.03	0.04	0.03
[1,2[	1.5	8	0.08	0.12	0.08
[2,3[	2.5	14	0.14	0.26	0.14
[3,4[	3.5	7	0.07	0.33	0.07
[4,5[	4.5	21	0.21	0.54	0.21
[5,6[	5.5	14	0.14	0.68	0.14
[6,7[	6.5	8	0.08	0.76	0.08
[7,8[	7.5	16	0.16	0.92	0.16
[8,9[	8.5	4	0.04	0.96	0.04
[9,10[	9.5	2	0.02	0.98	0.02
[10,11]	10.5	2	0.02	1	0.02

\begin{tabular}{lllllllll}
\hline
Frequency Table (Histogram) \tabularnewline
Bins & Midpoint & Abs. Frequency & Rel. Frequency & Cumul. Rel. Freq. & Density \tabularnewline
[-1,0[ & -0.5 & 1 & 0.01 & 0.01 & 0.01 \tabularnewline
[0,1[ & 0.5 & 3 & 0.03 & 0.04 & 0.03 \tabularnewline
[1,2[ & 1.5 & 8 & 0.08 & 0.12 & 0.08 \tabularnewline
[2,3[ & 2.5 & 14 & 0.14 & 0.26 & 0.14 \tabularnewline
[3,4[ & 3.5 & 7 & 0.07 & 0.33 & 0.07 \tabularnewline
[4,5[ & 4.5 & 21 & 0.21 & 0.54 & 0.21 \tabularnewline
[5,6[ & 5.5 & 14 & 0.14 & 0.68 & 0.14 \tabularnewline
[6,7[ & 6.5 & 8 & 0.08 & 0.76 & 0.08 \tabularnewline
[7,8[ & 7.5 & 16 & 0.16 & 0.92 & 0.16 \tabularnewline
[8,9[ & 8.5 & 4 & 0.04 & 0.96 & 0.04 \tabularnewline
[9,10[ & 9.5 & 2 & 0.02 & 0.98 & 0.02 \tabularnewline
[10,11] & 10.5 & 2 & 0.02 & 1 & 0.02 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296560&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][-1,0[[/C][C]-0.5[/C][C]1[/C][C]0.01[/C][C]0.01[/C][C]0.01[/C][/ROW]
[ROW][C][0,1[[/C][C]0.5[/C][C]3[/C][C]0.03[/C][C]0.04[/C][C]0.03[/C][/ROW]
[ROW][C][1,2[[/C][C]1.5[/C][C]8[/C][C]0.08[/C][C]0.12[/C][C]0.08[/C][/ROW]
[ROW][C][2,3[[/C][C]2.5[/C][C]14[/C][C]0.14[/C][C]0.26[/C][C]0.14[/C][/ROW]
[ROW][C][3,4[[/C][C]3.5[/C][C]7[/C][C]0.07[/C][C]0.33[/C][C]0.07[/C][/ROW]
[ROW][C][4,5[[/C][C]4.5[/C][C]21[/C][C]0.21[/C][C]0.54[/C][C]0.21[/C][/ROW]
[ROW][C][5,6[[/C][C]5.5[/C][C]14[/C][C]0.14[/C][C]0.68[/C][C]0.14[/C][/ROW]
[ROW][C][6,7[[/C][C]6.5[/C][C]8[/C][C]0.08[/C][C]0.76[/C][C]0.08[/C][/ROW]
[ROW][C][7,8[[/C][C]7.5[/C][C]16[/C][C]0.16[/C][C]0.92[/C][C]0.16[/C][/ROW]
[ROW][C][8,9[[/C][C]8.5[/C][C]4[/C][C]0.04[/C][C]0.96[/C][C]0.04[/C][/ROW]
[ROW][C][9,10[[/C][C]9.5[/C][C]2[/C][C]0.02[/C][C]0.98[/C][C]0.02[/C][/ROW]
[ROW][C][10,11][/C][C]10.5[/C][C]2[/C][C]0.02[/C][C]1[/C][C]0.02[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296560&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296560&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
[-1,0[	-0.5	1	0.01	0.01	0.01
[0,1[	0.5	3	0.03	0.04	0.03
[1,2[	1.5	8	0.08	0.12	0.08
[2,3[	2.5	14	0.14	0.26	0.14
[3,4[	3.5	7	0.07	0.33	0.07
[4,5[	4.5	21	0.21	0.54	0.21
[5,6[	5.5	14	0.14	0.68	0.14
[6,7[	6.5	8	0.08	0.76	0.08
[7,8[	7.5	16	0.16	0.92	0.16
[8,9[	8.5	4	0.04	0.96	0.04
[9,10[	9.5	2	0.02	0.98	0.02
[10,11]	10.5	2	0.02	1	0.02

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 100 ; par2 = 5 ; par3 = 2.5 ; par4 = 2 ; par5 = N ; par6 = 0 ;

Parameters (R input):

par1 = 100 ; par2 = 5 ; par3 = 2.5 ; par4 = 2 ; par5 = N ; par6 = 0 ; par7 = ; par8 = ;

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

library(MASS)
library(msm)
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