neodistr (version 0.1.2)

gmsnburr: GMSNBurr distribution

Description

To calculate density function, distribution function, 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)

Value

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

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.

Author

Achmad Syahrul Choir

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 \(\omega = {\frac{B(\alpha,\beta)}{\sqrt{2\pi}}}{{\left(1+{\frac{\beta}{\alpha}}\right)}^{\alpha+\beta}}{\left(\frac{\beta}{\alpha}\right)}^{-\beta}\)

References

Choir, A. S. (2020). The New Neo-Normal Distributions and their Properties. Dissertation. 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)
head(r)
hist(r, xlab = 'GMSNBurr random number', ylab = 'Frequency', 
main = 'Distribution of GMSNBurr Random Number ')