RBOLLG {ollg}

The Ristic-Balakrishnan Odd log-logistic family of distributions (RBOLL-G)

Description

Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Esmaeili et al. (2020) specified by the pdf

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

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

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

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

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

hrbollg(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

prbollg gives the distribution function, drbollg gives the density, qrbollg gives the quantile function, hrbollg gives the hazard function and rrbollg generates random variables from the The Ristic-Balakrishnan Odd log-logistic family of distributions (RBOLL-G) for baseline cdf G.

References

Esmaeili, H., Lak, F., Altun, E. (2020). The Ristic-Balakrishnan odd log-logistic family of distributions: Properties and Applications. Statistics, Optimization Information Computing, 8(1), 17-35.

Examples

x <- seq(0, 1, length.out = 21)
prbollg(x)
prbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
drbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(drbollg, -3, 3)
qrbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)

n <- 10
rrbollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)

hrbollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hrbollg, -3, 3)