GOLLG {ollg}

Generalized Odd log-logistic family of distributions (GOLL-G)

Description

Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Cordeiro et al. (2017) specified by the pdf

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

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

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

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

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

hgollg(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

pgollg gives the distribution function, dgollg gives the density, qgollg gives the quantile function, hgollg gives the hazard function and rgollg generates random variables from the Generalized Odd log-logistic family of distributions (GOLL-G) for baseline cdf G.

References

Cordeiro, G.M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E.M.M., Altun, E. (2017). The generalized odd log-logistic family of distributions : properties, regression models and applications. Journal of Statistical Computation and Simulation ,87(5),908-932.

Examples

x <- seq(0, 1, length.out = 21)
pgollg(x)
pgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
dgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dgollg, -3, 3)
qgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rgollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
hgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hgollg, -3, 3)