stukel: The Stukel distribution

In dnzmarcio/binreg: binreg R package

Description

Density, distribution function, quantile function and random generation function for the Prenctice distribution.

Usage

 dstukel(x, alpha)
 pstukel(q, alpha)
 qstukel(p, alpha)
 rstukel(n, alpha)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations.
alpha	vector of size two with shape parameters.

Details

The Stukel distribution with parameter m has distribution function given by

F(x) = 1/(1 + exp(-h(x,alpha)))

for alpha[1] > 0 and alpha[2] > 0, h(x,alpha) is

h(x,alpha) = (exp(alpha[1]*x) - 1)/alpha[1] if (x >= 0) and (alpha[1] > 0) x if (x >= 0) and (alpha[1] = 0) -log(1 - alpha[1]*x)/alpha[1] if (x >= 0) and (alpha[1] < 0) -(exp(-alpha[2]*x) - 1)/alpha[2] if (x < 0) and (alpha[2] > 0) x if (x < 0) and (alpha[2] = 0) log(1 + alpha[2]*eta)/alpha[2] if (x < 0) and (alpha[2] < 0)

Value

'dstukel' gives the density, 'pstukel' gives the distribution function, 'qstukel' gives the quantile function, and 'rstukel' generates random deviates.

References

Stukel, T. A. (1988) Generalized logistic models. Journal of the American Statistical Association, pp. 426-431.

Examples

  set.seed(1234)
  alpha <- c(2,0.5)
  x <- seq(-5,5,0.01)
  y <- pstukel(x,alpha)
  plot(x,y,type="l",xlab="x",ylab="pstukel")

dnzmarcio/binreg documentation built on May 15, 2019, 9:41 a.m.