gmsnburr: GMSNBurr distribution In neodistr: Neo-Normal Distribution

 gmsnburr R Documentation

GMSNBurr distribution

Description

To calculate density function, distribution funcion, quantile function, and build data from random generator function for the GMSNBurr Distribution.

Usage

dgmsnburr(x, mu = 0, sigma = 1, alpha = 1, beta = 1, log = FALSE)

pgmsnburr(
q,
mu = 0,
sigma = 1,
alpha = 1,
beta = 1,
lower.tail = TRUE,
log.p = FALSE
)

qgmsnburr(
p,
mu = 0,
sigma = 1,
alpha = 1,
beta = 1,
lower.tail = TRUE,
log.p = FALSE
)

rgmsnburr(n, mu = 0, sigma = 1, alpha = 1, beta = 1)


Arguments

 x, q vector of quantiles. mu a location parameter. sigma a scale parameter. alpha a shape parameter. beta a shape parameter. log, log.p logical; if TRUE, probabilities p are given as log(p) The default value of this parameter is FALSE. lower.tail logical;if TRUE (default), probabilities are P\left[ X\leq x\right], otherwise, P\left[ X>x\right] . p vectors of probabilities. n number of observations.

Details

GMSNBurr Distribution

The GMSNBurr distribution with parameters \mu, \sigma,\alpha, and \beta has density:

f(x |\mu,\sigma,\alpha,\beta) = {\frac{\omega}{{B(\alpha,\beta)}\sigma}}{{\left(\frac{\beta}{\alpha}\right)}^\beta} {{\exp{\left(-\beta \omega {\left(\frac{x-\mu}{\sigma}\right)}\right)} {{\left(1+{\frac{\beta}{\alpha}} {\exp{\left(-\omega {\left(\frac{x-\mu}{\sigma}\right)}\right)}}\right)}^{-(\alpha+\beta)}}}}

where -\infty<x<\infty, -\infty<\mu<\infty, \sigma>0, \alpha>0, \beta>0 and \omega = {\frac{B(\alpha,\beta)}{\sqrt{2\pi}}}{{\left(1+{\frac{\beta}{\alpha}}\right)}^{\alpha+\beta}}{\left(\frac{\beta}{\alpha}\right)}^{-\beta}

Value

dgmsnburr gives the density , pgmasnburr gives the distribution function, qgmsnburr gives quantiles function, rgmsnburr generates random numbers.

References

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Disertation. Institut Teknologi Sepuluh Nopember.

Iriawan, N. (2000). Computationally Intensive Approaches to Inference in Neo-Normal Linear Models. Curtin University of Technology.

Examples

library("neodistr")
dgmsnburr(0, mu=0, sigma=1, alpha=1,beta=1)
pgmsnburr(4, mu=0, sigma=1, alpha=1, beta=1)
qgmsnburr(0.4, mu=0, sigma=1, alpha=1, beta=1)
r=rgmsnburr(10000, mu=0, sigma=1, alpha=1, beta=1)