ZBOLLG {ollg}

The Zografos-Balakrishnan Odd log-logistic family of distributions (ZBOLL-G)

Description

Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Cordeiro et al. (2016) specified by the pdf

f=\frac{\alpha\,g\,G^{\alpha-1}\bar{G}^{\alpha-1}}{\Gamma(\beta)[G^\alpha+\bar{G}^\alpha]^2}\,\{-\log[1-\frac{G^\alpha}{G^\alpha+\bar{G}^\alpha}]\}^{\beta-1}

for G any valid continuous cdf , \bar{G}=1-G, g the corresponding pdf, \Gamma(\beta) the Gamma funcion, \alpha > 0, the first shape parameter, and \beta > 0, the second shape parameter.

Usage

pzbollg(x, alpha = 1, beta = 1, G = pnorm, ...)

dzbollg(x, alpha = 1, beta = 1, G = pnorm, ...)

qzbollg(q, alpha = 1, beta = 1, G = pnorm, ...)

rzbollg(n, alpha = 1, beta = 1, G = pnorm, ...)

hzbollg(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

pzbollg gives the distribution function, dzbollg gives the density, qzbollg gives the quantile function, hzbollg gives the hazard function and rzbollg generates random variables from the The Zografos-Balakrishnan Odd log-logistic family of distributions (ZBOLL-G) for baseline cdf G.

References

Cordeiro, G. M., Alizadeh, M., Ortega, E. M., Serrano, L. H. V. (2016). The Zografos-Balakrishnan odd log-logistic family of distributions: Properties and Applications. Hacettepe Journal of Mathematics and Statistics, 45(6), 1781-1803. .

Examples

x <- seq(0, 1, length.out = 21)
pzbollg(x)
pzbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
dzbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dzbollg, -3, 3)
qzbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rzbollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
hzbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hzbollg, -3, 3)