ollg (version 1.0.0)

ANOLLG: A New Odd log-logistic family of distributions (ANOLL-G)

Description

Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Haghbin et al. (2017) specified by the pdf $$f=\frac{\alpha\beta\,g\,\bar{G}^{\alpha\beta-1}[1-\bar{G}^\alpha]^{\beta-1}}{\{[1-\bar{G}^\alpha]^\beta+\bar{G}^{\alpha\beta}\}^2}$$ 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

panollg(x, alpha = 1, beta = 1, G = pnorm, ...)
danollg(x, alpha = 1, beta = 1, G = pnorm, ...)
qanollg(q, alpha = 1, beta = 1, G = pnorm, ...)
ranollg(n, alpha = 1, beta = 1, G = pnorm, ...)
hanollg(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

panollg gives the distribution function, danollg gives the density, qanollg gives the quantile function, hanollg gives the hazard function and ranollg generates random variables from the A New Odd log-logistic family of distributions (ANOLL-G) for baseline cdf G.

References

Haghbin, Hossein, et al. "A new generalized odd log-logistic family of distributions." Communications in Statistics-Theory and Methods 46.20(2017): 9897-9920.

Examples

# NOT RUN {
x <- seq(0, 1, length.out = 21)
panollg(x)
panollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
danollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(danollg, -3, 3)
qanollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
n <- 10
ranollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
hanollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2)
curve(hanollg, -3, 3)
# }