| MOOLLG {ollg} | R Documentation |
Marshal-Olkin Odd log-logistic family of distributions (MOOLL-G)
Description
Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Gleaton et al. (2010) specified by the pdf
f=\frac{\alpha\beta\,g\,G^{\alpha-1}\bar{G}^{\alpha-1}}{[G^\alpha+\beta\,\bar{G}^\alpha]^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
pmoollg(x, alpha = 1, beta = 1, G = pnorm, ...)
dmoollg(x, alpha = 1, beta = 1, G = pnorm, ...)
qmoollg(q, alpha = 1, beta = 1, G = pnorm, ...)
rmoollg(n, alpha = 1, beta = 1, G = pnorm, ...)
hmoollg(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
pmoollg gives the distribution function,
dmoollg gives the density,
qmoollg gives the quantile function,
hmoollg gives the hazard function and
rmoollg generates random variables from the Marshal-Olkin Odd log-logistic family of
distributions (MOOLL-G) for baseline cdf G.
References
Gleaton, J. U., Lynch, J. D. (2010). Extended generalized loglogistic families of lifetime distributions with an application. J. Probab. Stat.Sci, 8(1), 1-17.
Examples
x <- seq(0, 1, length.out = 21)
pmoollg(x)
pmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
dmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(dmoollg, -3, 3)
qmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
rmoollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
hmoollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hmoollg, -3, 3)