| KwOLLG {ollg} | R Documentation |
Kumaraswamy Odd log-logistic family of distributions (KwOLL-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{a\,b\,\alpha\,g\,G^{a\,\alpha-1}\bar{G}^{\alpha-1}}{[G^\alpha+\bar{G}^\alpha]^{a+1}}\times \{1-[\frac{G^\alpha}{G^\alpha+\bar{G}^\alpha}]^a\}^{b-1}
for G any valid continuous cdf , \bar{G}=1-G, g the corresponding pdf, a, b > 0, the shape parameter, \alpha > 0, the first shape parameter.
Usage
pkwollg(x, alpha = 1, a = 1, b = 1, G = pnorm, ...)
dkwollg(x, alpha = 1, a = 1, b = 1, G = pnorm, ...)
qkwollg(q, alpha = 1, a = 1, b = 1, G = pnorm, ...)
rkwollg(n, alpha = 1, a = 1, b = 1, G = pnorm, ...)
hkwollg(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
pkwollg gives the distribution function,
dkwollg gives the density,
qkwollg gives the quantile function,
hkwollg gives the hazard function and
rkwollg generates random variables from the Kumaraswamy Odd log-logistic family of
distributions (KwOLL-G) for baseline cdf G.
References
Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G. M., Ortega, E. M., Pescim, R. R. (2015). A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications. Hacettepe Journal of Mathematics and Statistics, 44(6), 1491-1512.
Examples
x <- seq(0, 1, length.out = 21)
pkwollg(x)
pkwollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
dkwollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dkwollg, -3, 3)
qkwollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rkwollg(n, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
hkwollg(x, alpha = 2, a = 2, b = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hkwollg, -3, 3)