# [R] Beta distribution approximate to Normal distribution

JLucke at ria.buffalo.edu JLucke at ria.buffalo.edu
Tue Sep 15 18:15:23 CEST 2015

```Scratch the  rchisq  (it should have been sqrt(rchisq), but that doesn't
help.).

Use the truncated normal

u <- 3; a <- 2;
N <- 100
x <- numeric(N)
for (i in 1:N){
repeat{
if( (x[i] <- rnorm(1, u, a)) >= 0 ) break
}
}

or the folded normal

abs(rnorm(N, u, a)),

They give similar results.
The  code for the truncated normal allows you to set any truncation point.

Joe

(Ted Harding) <Ted.Harding at wlandres.net>
Sent by: "R-help" <r-help-bounces at r-project.org>
09/15/2015 11:12 AM
Ted.Harding at wlandres.net

To
"r-help at r-project.org" <r-help at r-project.org>,
cc
Chien-Pang Chin <chienpang.c at gmail.com>
Subject
Re: [R] Beta distribution approximate to Normal distribution

Using non-central chi-squared (especially with df=1) is unlikely
to generate random numbers anywhere near a Normal distribution
(see below).

And "rchisq(100, df=1, ncp=u/a)" won't work anyway with u<0,
since ncp must be >= 0 (if < 0 then all are NA).

Better to shoot straight for the target (truncated Normal), though
several shots are likely to be required! For example (code which
spells it out), taking u=3 and a=2:

n <- 100
u <- 3 ; a <- 2
x <- NULL
N <- length(x)
while(N < n){
x <- c(x,rnorm(n,mean=u,sd=a))
x <- x[x>0]
N <- length(x)
}
x <- x[1:n]

Comparison with non-central chi-squared:

y <- rchisq(100, df=1, ncp=u/a)
hist(x)
hist(y)

On 15-Sep-2015 13:26:44 JLucke at ria.buffalo.edu wrote:
> Your question makes no sense as stated.  However, guessing at what you
> want, you should  perhaps consider the non-central chi-square density
with
> 1 df and ncp = u/a, i.e,
>
> rchisq(100, df=1, ncp=u/a)
>
> Joe
> Joseph F. Lucke, PhD
> Senior Statistician
> Research Institute on Addictions
> University at Buffalo
> State University of New York
> 1021 Main Street
> Buffalo, NY  14203-1016
>
> Chien-Pang Chin <chienpang.c at gmail.com>
> Sent by: "R-help" <r-help-bounces at r-project.org>
> 09/15/2015 06:58 AM
>
> To
> "r-help at r-project.org" <r-help at r-project.org>,
>
> Subject
> [R] Beta distribution approximate to Normal distribution
>
> Hi,
> I need to generate 1000 numbers from N(u, a^2), however I don't
> want to include 0 and negative values. How can I use beta distribution
> approximate to N(u, a^2) in R.
>
> Thx for help

-------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 15-Sep-2015  Time: 16:12:35
This message was sent by XFMail

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