OLLLG {ollg}

Odd log-logistic logarithmic family of distributions (OLLL-G)

Description

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

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

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

Usage

polllg(x, alpha = 1, beta = 0.1, G = pnorm, ...)

dolllg(x, alpha = 1, beta = 0.1, G = pnorm, ...)

qolllg(q, alpha = 1, beta = 0.1, G = pnorm, ...)

rolllg(n, alpha = 1, beta = 0.1, G = pnorm, ...)

holllg(x, alpha = 1, beta = 0.1, 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, between 0 and 1, the default is 0.1.

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

polllg gives the distribution function, dolllg gives the density, qolllg gives the quantile function, holllg gives the hazard function and rolllg generates random variables from the Odd log-logistic logarithmic family of distributions (OLLL-G) for baseline cdf G.

References

Alizadeh, M., MirMostafee, S. M. T. K., Ortega, E. M., Ramires, T. G., Cordeiro, G. M. (2017). The odd log-logistic logarithmic generated family of distributions with applications in different areas. Journal of Statistical Distributions and Applications, 4(1), 1-25.

Examples

x <- seq(0, 1, length.out = 21)
polllg(x)
polllg(x, alpha = 2, beta = .2, G = pbeta, shape1 = 1, shape2 = 2)

dolllg(x, alpha = 2, beta = .2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dolllg, -3, 3)
qolllg(x, alpha = 2, beta = .2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rolllg(n, alpha = 2, beta = .2, G = pbeta, shape1 = 1, shape2 = 2)
holllg(x, alpha = 2, G = pbeta, beta = .2, shape1 = 1, shape2 = 2)
curve(holllg, -3, 3)