ollg (version 1.0.0)

OLLG: 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

# NOT RUN {
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)
# }