msnburr {neodistr}

MSNBurr Distribution

Description

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

Usage

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

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

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

rmsnburr(n, mu = 0, sigma = 1, alpha = 1)

Arguments

x, q

vector of quantiles.

mu

a location parameter.

sigma

a scale parameter.

alpha

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

MSNBurr Distribution

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

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

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

Value

dmsnburr gives the density , pmsnburr gives the distribution function, qmsnburr gives quantiles function, rmsnburr generates random numbers.

Author(s)

Achmad Syahrul Choir and Nur Iriawan

References

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

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

Examples

library("neodistr")
dmsnburr(0, mu=0, sigma=1, alpha=0.1)
plot(function(x) dmsnburr(x, alpha=0.1), -20, 3,
main = "Left Skew MSNBurr Density ",ylab="density")
pmsnburr(7, mu=0, sigma=1, alpha=1)
qmsnburr(0.6, mu=0, sigma=1, alpha=1)
r<- rmsnburr(10000, mu=0, sigma=1, alpha=1)
head(r)
hist(r, xlab = 'MSNBurr random number', ylab = 'Frequency', 
main = 'Distribution of MSNBurr Random Number ')