msnburr2a {neodistr}

MSNBurr-IIa distribution.

Description

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

Usage

dmsnburr2a(x, mu = 0, sigma = 1, alpha = 1, log = FALSE)

pmsnburr2a(q, mu = 0, sigma = 1, alpha = 1, lower.tail = TRUE, log.p = FALSE)

qmsnburr2a(p, mu = 0, sigma = 1, alpha = 1, lower.tail = TRUE, log.p = FALSE)

rmsnburr2a(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-IIa Distribution

The MSNBurr-IIa 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

dmsnburr2a gives the density, pmsnburr2a gives the distribution function, qmsnburr2a gives the quantile function and rmsnburr2a generates random numbers.

Author(s)

Achmad Syahrul Choir and Nur Iriawan

References

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

Examples

library("neodistr")
dmsnburr2a(7, mu=0, sigma=1, alpha=0.1)
plot(function(x) dmsnburr2a(x, alpha=0.1), -3, 20,
main = "Right Skew MSNBurr-IIa Density ",ylab="density")
p=pmsnburr2a(4, mu=0, sigma=1, alpha=1)
p
q=qmsnburr2a(p, mu=0, sigma=1, alpha=1)
q
qmsnburr2a(0.5, mu=0, sigma=1, alpha=1)
r=rmsnburr2a(10000, mu=0, sigma=1, alpha=0.1)
head(r)
hist(r, xlab = 'MSNBurr random number', ylab = 'Frequency', 
main = 'Distribution of MSNBurr-IIa Random Number ')