ollg (version 1.0.0)

MOOLLG: Marshal-Olkin Odd log-logistic family of distributions (MOOLL-G)

Description

Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Gleaton et al. (2010) specified by the pdf $$f=\frac{\alpha\beta\,g\,G^{\alpha-1}\bar{G}^{\alpha-1}}{[G^\alpha+\beta\,\bar{G}^\alpha]^2}$$ for \(G\) any valid continuous cdf , \(\bar{G}=1-G\), \(g\) the corresponding pdf, \(\alpha > 0\), the first shape parameter, and \(\beta > 0\), the second shape parameter.

Usage

pmoollg(x, alpha = 1, beta = 1, G = pnorm, ...)
dmoollg(x, alpha = 1, beta = 1, G = pnorm, ...)
qmoollg(q, alpha = 1, beta = 1, G = pnorm, ...)
rmoollg(n, alpha = 1, beta = 1, G = pnorm, ...)
hmoollg(x, alpha = 1, beta = 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.

beta

the value of the second 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

pmoollg gives the distribution function, dmoollg gives the density, qmoollg gives the quantile function, hmoollg gives the hazard function and rmoollg generates random variables from the Marshal-Olkin Odd log-logistic family of distributions (MOOLL-G) for baseline cdf G.

References

Gleaton, J. U., Lynch, J. D. (2010). Extended generalized loglogistic families of lifetime distributions with an application. J. Probab. Stat.Sci, 8(1), 1-17.

Examples

# NOT RUN {
x <- seq(0, 1, length.out = 21)
pmoollg(x)
pmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
dmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dmoollg, -3, 3)
qmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rmoollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
hmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hmoollg, -3, 3)
# }