distrib {genlogis}

The Generalized logistic distribution

Description

Density, distribution function, quantile function and random generation a generalized logistic distribution.

Usage

pgenlog(q, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0, lower.tail = TRUE)

dgenlog(x, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0)

qgenlog(k, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0, lower.tail = TRUE)

rgenlog(n, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0)

Arguments

a, b, p

parameters \ge 0, with restrictions.*

mu

mu parameter

lower.tail

logical; if TRUE (default), probabilities are P[X \le x] otherwise, P[X > x].

x, q

vector of quantiles.

k

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required

Details

The used distribution for this package is given by:

f(x) = ((a + b*(1+p)*(|x-mu|^p))*exp(-(x-mu)*(a+b*(|x-mu|^p)))) / ((exp(-(x-mu)*(a + b* (|x-mu|^p)))+1)^2)

The default values for a, b, p and mu produces a function with mean 0 and variance close to 1.

*Restrictions:

If p equals to 0, b or a must be 0 otherwise there is identifiability problem.

The distribution is not defined for a and b equal to 0 simultaneously.

Value

dgenlog gives the density, pgenlog gives the distribution function, qgenlog gives the quantile function, and rgenlog generates random deviates.

The length of the result is determined by n for rgenlog, and is the maximum of the lengths of the numerical arguments for the other functions.

References

Rathie, P. N. and Swamee, P. K (2006) On a new invertible generalized logistic distribution approximation to normal distribution, Technical Research Report in Statistics, 07/2006, Dept. of Statistics, Univ. of Brasilia, Brasilia, Brazil.

Examples

pgenlog(0.5) 
curve(dgenlog(x), xlim = c(-3,3)) 

rgenlog(100) 

qgenlog(0.95)