| NOLLG {ollg} | R Documentation |
New Odd log-logistic family of distributions (NOLL-G)
Description
Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Alizadeh et al. (2019) specified by the pdf
f=\frac{g\,G^{\alpha-1}\bar{G}^{\beta-1}[\alpha+(\beta-\alpha)G]}{[G^\alpha+\bar{G}^\beta]^2}
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
pnollg(x, alpha = 1, beta = 1, G = pnorm, ...)
dnollg(x, alpha = 1, beta = 1, G = pnorm, ...)
qnollg(q, alpha = 1, beta = 1, G = pnorm, ...)
rnollg(n, alpha = 1, beta = 1, G = pnorm, ...)
hnollg(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
pnollg gives the distribution function,
dnollg gives the density,
qnollg gives the quantile function,
hnollg gives the hazard function and
rnollg generates random variables from the New Odd log-logistic family of
distributions (NOLL-G) for baseline cdf G.
References
Alizadeh, M., Altun, E., Ozel, G., Afshari, M., Eftekharian, A. (2019). A new odd log-logistic lindley distribution with properties and applications. Sankhya A, 81(2), 323-346.
Examples
x <- seq(0, 1, length.out = 21)
pnollg(x)
pnollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
dnollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dnollg, -3, 3)
qnollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rnollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
hnollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hnollg, -3, 3)