BOLLG {ollg}

The beta Odd log-logistic family of distributions (BOLL-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^{a\,\alpha-1}\bar{G}^{b\,\alpha-1}}{B(a,b)[G^\alpha+\bar{G}^\alpha]^{a+b}}

for G any valid continuous cdf , \bar{G}=1-G, g the corresponding pdf, B(a, b), the beta function, a, b > 0, the shape parameter, \alpha > 0, the first shape parameter.

Usage

pbollg(x, alpha = 1, a = 1, b = 1, G = pnorm, ...)

dbollg(x, alpha = 1, a = 1, b = 1, G = pnorm, ...)

qbollg(q, alpha = 1, a = 1, b = 1, G = pnorm, ...)

rbollg(n, alpha = 1, a = 1, b = 1, G = pnorm, ...)

hbollg(x, alpha = 1, a = 1, b = 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.

a

the value of the shape parameter, must be positive, the default is 1.

b

the value of the 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

pbollg gives the distribution function, dbollg gives the density, qbollg gives the quantile function, hbollg gives the hazard function and rbollg generates random variables from the The beta Odd log-logistic family of distributions (BOLL-G) for baseline cdf G.

References

Cordeiro, G. M., Alizadeh, M., Tahir, M. H., Mansoor, M., Bourguignon, M., Hamedani, G. G. (2016). The beta odd log-logistic generalized family of distributions. Hacettepe Journal of Mathematics and Statistics, 45(4), 1175-1202.

Examples

x <- seq(0, 1, length.out = 21)
pbollg(x)
pbollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
dbollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dbollg, -3, 3)
qbollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rbollg(n, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
hbollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hbollg, -3, 3)