OLLLG | R Documentation |
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{αβ\,g\,G^{α-1}\bar{G}^{α-1}}{-[G^α+\bar{G}^α][(1-β)\,G^α+\bar{G}^α]\log(1-β)}
for G any valid continuous cdf , \bar{G}=1-G, g the corresponding pdf, α > 0, the first shape parameter, and 0 < β < 1, the second shape parameter.
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, ...)
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. |
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.
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.
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)
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