OBuG {ollg}

Odd Burr generated family of distributions (OBu-G)

Description

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

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

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

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

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

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

hobug(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

pobug gives the distribution function, dobug gives the density, qobug gives the quantile function, hobug gives the hazard function and robug generates random variables from the Odd Burr generated family of distributions (OBu-G) for baseline cdf G.

References

Alizadeh, M., Cordeiro, G. M., Nascimento, A. D., Lima, M. D. C. S., Ortega, E. M. (2017). Odd-Burr generalized family of distributions with some applications. Journal of statistical computation and simulation, 87(2), 367-389.

Examples

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

dobug(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dobug, -3, 3)
qobug(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
robug(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
hobug(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hobug, -3, 3)