Runuran (version 0.40)

udnorm: UNU.RAN object for Normal distribution

Description

Create UNU.RAN object for a Normal (Gaussian) distribution with mean equal to mean and standard deviation to sd.

[Distribution] -- Normal (Gaussian).

Usage

udnorm(mean=0, sd=1, lb=-Inf, ub=Inf)

Value

An object of class "unuran.cont".

Arguments

mean

mean of distribution.

sd

standard deviation.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The normal distribution with mean \(\mu\) and standard deviation \(\sigma\) has density $$ f(x) = \frac{1}{\sqrt{2\pi}\sigma} e^{-(x-\mu)^2/2\sigma^2} $$ where \(\mu\) is the mean of the distribution and \(\sigma\) the standard deviation.

The domain of the distribution can be truncated to the interval (lb,ub).

References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions, Volume 1. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 13, p. 80.

See Also

unuran.cont.

Examples

## Create distribution object for standard normal distribution
distr <- udnorm()
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)

## Create distribution object for positive normal distribution
distr <- udnorm(lb=0, ub=Inf)
## ... and draw a sample
gen <- pinvd.new(distr)
x <- ur(gen,100)