udlogis function

UNU.RAN object for Logistic distribution

UNU.RAN object for Logistic distribution

Create UNU.RAN object for a Logistic distribution with parameters location and scale.

[Distribution] -- Logistic.

udlogis(location=0, scale=1, lb=-Inf, ub=Inf)

Arguments

  • location: location parameter.
  • scale: (strictly positive) scale parameter.
  • lb: lower bound of (truncated) distribution.
  • ub: upper bound of (truncated) distribution.

Details

The Logistic distribution with location =m= m and scale =s= s has distribution function

F(x)=11+e−(x−μ)/σF(x)=1/(1+exp(−(x−m)/s)) F(x) = \frac{1}{1 + e^{-(x-\mu)/\sigma}}F(x) = 1 / (1 + exp(-(x-m)/s))

and density

f(x)=1σe(x−μ)/σ(1+e(x−μ)/σ)2f(x)=1/sexp((x−m)/s)(1+exp((x−m)/s))−2. f(x) = \frac{1}{\sigma}\frac{e^{(x-\mu)/\sigma}}{(1 + e^{(x-\mu)/\sigma})^2}f(x) = 1/s exp((x-m)/s) (1 + exp((x-m)/s))^-2.

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

Returns

An object of class "unuran.cont".

See Also

unuran.cont.

References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1995): Continuous Univariate Distributions, Volume 2. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 23, p. 115.

Author(s)

Josef Leydold and Wolfgang H"ormann unuran@statmath.wu.ac.at .

Examples

## Create distribution object for standard logistic distribution
distr <- udlogis()
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)
Runuran packageRead PDF manual
  • Maintainer: Josef Leydold
  • License: GPL (>= 2)
  • Last published: 2025-04-07

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