| OLLG {ollg} | R Documentation |
Odd log-logistic family of distributions (OLL-G)
Description
Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Gleaton et al. (2006) specified by the pdf
f=\frac{\alpha\,g\,G^{\alpha-1}\bar{G}^{\alpha-1}}{[G^\alpha+\bar{G}^\alpha]^2}
for G any valid continuous cdf , \bar{G}=1-G, g the corresponding pdf, \alpha > 0, the first shape parameter.
Usage
pollg(x, alpha = 1, G = pnorm, ...)
dollg(x, alpha = 1, G = pnorm, ...)
qollg(q, alpha = 1, G = pnorm, ...)
rollg(n, alpha = 1, G = pnorm, ...)
hollg(x, alpha = 1, G = pnorm, ...)
Arguments
x |
scaler or vector of values at which the pdf or cdf needs to be computed. |
alpha |
the value of the first shape parameter, must be positive, the default is 1. |
G |
A baseline continuous cdf. |
... |
The baseline cdf parameters. |
q |
scaler or vector of probabilities at which the quantile needs to be computed. |
n |
number of random numbers to be generated. |
Value
pollg gives the distribution function,
dollg gives the density,
qollg gives the quantile function,
hollg gives the hazard function and
rollg generates random variables from the Odd log-logistic family of
distributions (OLL-G) for baseline cdf G.
References
Gleaton, J. U., Lynch, J. D. (2006). Properties of generalized log-logistic families of lifetime distributions. Journal of Probability and Statistical Science, 4(1), 51-64.
Examples
x <- seq(0, 1, length.out = 21)
pollg(x)
pollg(x, alpha = 2, G = pbeta, shape1 = 1, shape2 = 2)
dollg(x, alpha = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dollg, -3, 3)
qollg(x, alpha = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rollg(n, alpha = 2, G = pbeta, shape1 = 1, shape2 = 2)
hollg(x, alpha = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hollg, -3, 3)