EOLLG {ollg}

Exponentiated Odd log-logistic family of distributions (EOLL-G)

Description

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

f=\frac{\alpha\beta\,g\,G^{\alpha\beta-1}\bar{G}^{\alpha-1}}{[G^\alpha+\bar{G}^\alpha]^{\beta+1}}

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

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

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

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

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

heollg(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

peollg gives the distribution function, deollg gives the density, qeollg gives the quantile function, heollg gives the hazard function and reollg generates random variables from the Exponentiated Odd log-logistic family of distributions (EOLL-G) for baseline cdf G.

References

ALIZADEH, Morad; TAHMASEBI, Saeid; HAGHBIN, Hossein. The exponentiated odd log-logistic family of distributions: Properties and applications. Journal of Statistical Modelling: Theory and Applications, 2020, 1. Jg., Nr. 1, S. 29-52.

Examples

x <- seq(0, 1, length.out = 21)
peollg(x)
peollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
deollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(deollg, -3, 3)
qeollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
reollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
heollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(heollg, -3, 3)