Runuran (version 0.21.0)

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)

Arguments

mean

mean of distribution.

sd

standard deviation.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Value

• An object of class "unuran.cont".

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)