::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) generates a specified number of random series for the Log-Normal distribution. The parameters allow you to specify the length of the dataseries to be generated, the mean of the distribution, and the standard error of the distribution.

The generated random numbers are listed in a table (if possible). In addition a histogram is shown of the estimated mean and standard deviation (over all simulated series)

This R module is an illustration of the central limit theorem.

Click here to edit the underlying code of this R Module.

Send output to:
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Number of values (?)
Mean (?)
S.D. (?)
Color code (?)
List Random Numbers in table? (?)
Number of bins (?)
Number of series (?)
Chart options
Width:
Height:

Click here to edit the underlying code of this R Module.

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Cite this software as:

Wessa P., (2008), Random Number Generator for the Log-Normal Distribution (v1.0.4) in Free Statistics Software (v1.1.22-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_rnglnorm.wasp/

The R code is based on :

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988), The New S Language, Wadsworth & Brooks/Cole.

Source code of R module
1	library(MASS)
2	par1 <- as.numeric(par1)
3	par2 <- as.numeric(par2)
4	par2 <- round(par2,2) #rounded (we want to be able to display 10 columns)
5	par3 <- as.numeric(par3)
6	par3 <- round(par3,2) #rounded (we want to be able to display 10 columns)
7	par4 <- as.numeric(par4)
8	if (par6 == "0") par6 = "Sturges" else par6 <- as.numeric(par6)
9	par7 <- as.numeric(par7)
10	x <- array(NA,dim=c(par7,par1))
11	rest.mean <- array(NA,dim=c(par7))
12	rest.sd <- array(NA,dim=c(par7))
13	rsd.mean <- array(NA,dim=c(par7))
14	rsd.sd <- array(NA,dim=c(par7))
15	for (i in 1:par7)
16	{
17	x[i,] <- rlnorm(par1,par2,par3)
18	x[i,] <- as.ts(x[i,]) #otherwise the fitdistr function does not work properly
19	dum <- fitdistr(x[i,],"log-normal")
20	rest.mean[i] <- dum$estimate[1]
21	rest.sd[i] <- dum$estimate[2]
22	rsd.mean[i] <- dum$sd[1]
23	rsd.sd[i] <- dum$sd[2]
24	}
25	nc <- par7
26	if (nc > 10) nc = 10
27	if (par5 == "Y")
28	{
29	load(file="createtable")
30	a<-table.start()
31	a<-table.row.start(a)
32	a<-table.element(a,"Index",1,TRUE)
33	for (j in 1:nc)
34	{
35	a<-table.element(a,paste("X",j),1,TRUE)
36	}
37	a<-table.row.end(a)
38	if (nc < par7)
39	{
40	a<-table.row.start(a)
41	a<-table.element(a,"Note: only the first 10 series are displayed",nc+1,TRUE)
42	a<-table.row.end(a)
43	}
44	for (i in 1:par1)
45	{
46	a<-table.row.start(a)
47	a<-table.element(a,i,header=TRUE)
48	for (j in 1:nc)
49	{
50	a<-table.element(a,round(x[j,i],2))
51	}
52	a<-table.row.end(a)
53	}
54	a<-table.end(a)
55	table.save(a,file="mytable1.tab")
56	}
57	load(file="createtable")
58	a<-table.start()
59	a<-table.row.start(a)
60	a<-table.element(a,"Parameter",1,TRUE)
61	for (j in 1:nc)
62	{
63	a<-table.element(a,paste("X",j,sep=""),1,TRUE)
64	}
65	a<-table.row.end(a)
66	a<-table.row.start(a)
67	a<-table.element(a," ",1,TRUE)
68	for (j in 1:nc)
69	{
70	a<-table.element(a,"(SD)",1,TRUE)
71	}
72	a<-table.row.end(a)
73	a<-table.row.start(a)
74	a<-table.element(a,"# simulated values",header=TRUE)
75	for (j in 1:nc)
76	{
77	a<-table.element(a,par1)
78	}
79	a<-table.row.end(a)
80	a<-table.row.start(a)
81	a<-table.element(a,"true mean",header=TRUE)
82	for (j in 1:nc)
83	{
84	a<-table.element(a,par2)
85	}
86	a<-table.row.end(a)
87	a<-table.row.start(a)
88	a<-table.element(a,"true standard deviation",header=TRUE)
89	for (j in 1:nc)
90	{
91	a<-table.element(a,par3)
92	}
93	a<-table.row.end(a)
94	a<-table.row.start(a)
95	a<-table.element(a,"mean",header=TRUE)
96	for (j in 1:nc)
97	{
98	a<-table.element(a,round(rest.mean[j],2))
99	}
100	a<-table.row.end(a)
101	a<-table.row.start(a)
102	a<-table.element(a," ",header=TRUE)
103	for (j in 1:nc)
104	{
105	a<-table.element(a,round(rsd.mean[j],2))
106	}
107	a<-table.row.end(a)
108	a<-table.row.start(a)
109	a<-table.element(a,"standard deviation",header=TRUE)
110	for (j in 1:nc)
111	{
112	a<-table.element(a,round(rest.sd[j],2))
113	}
114	a<-table.row.end(a)
115	a<-table.row.start(a)
116	a<-table.element(a," ",header=TRUE)
117	for (j in 1:nc)
118	{
119	a<-table.element(a,round(rsd.sd[j],2))
120	}
121	a<-table.row.end(a)
122	a<-table.end(a)
123	table.save(a,file="mytable.tab")
124	bitmap(file="test0.png")
125	myhist<-hist(x[1,],col=par4,breaks=par6,main="Histogram of 1st simulated series",ylab="density",xlab="simulated values",freq=F)
126	dev.off()
127	bitmap(file="test1.png")
128	myhist<-hist(rest.mean[],col=par4,breaks=par6,main="Histogram of Estimated Means",ylab="density",xlab="estimated means",freq=F)
129	x <- rest.mean[]
130	dummean <- mean(x)
131	dumsd <- sd(x)
132	curve(1/(dumsd*sqrt(2*pi))*exp(-1/2*((x-dummean)/dumsd)^2),min(x),max(x),add=T)
133	dev.off()
134	bitmap(file="test2.png")
135	myhist<-hist(rest.sd[],col=par4,breaks=par6,main="Histogram of Estimated SDs",ylab="density",xlab="estimated standard deviations",freq=F)
136	x <- rest.sd[]
137	dummean <- mean(x)
138	dumsd <- sd(x)
139	curve(1/(dumsd*sqrt(2*pi))*exp(-1/2*((x-dummean)/dumsd)^2),min(x),max(x),add=T)
140	dev.off()

To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.22-r6, URL http://www.wessa.net/

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Software Version : 1.1.22-r6
Algorithms & Software : Prof. dr. P. Wessa
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