KwOLLG: Kumaraswamy Odd log-logistic family of distributions...

In ollg: Computes some Measures of OLL-G Family of Distributions

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\,α\,g\,G^{a\,α-1}\bar{G}^{α-1}}{[G^α+\bar{G}^α]^{a+1}}\times \{1-[\frac{G^α}{G^α+\bar{G}^α}]^a\}^{b-1}

for G any valid continuous cdf , \bar{G}=1-G, g the corresponding pdf, a, b > 0, the shape parameter, α > 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)

ollg documentation built on March 18, 2022, 6:57 p.m.