alcdf: cdf of an asymmetric Laplace distribution

In bqror: Bayesian Quantile Regression for Ordinal Models

cdf of an asymmetric Laplace distribution

Description

This function computes the cumulative distribution function (cdf) of an asymmetric Laplace (AL) distribution.

Usage

alcdf(x, mu, sigma, p)

Arguments

x	scalar value.
mu	location parameter of an AL distribution.
sigma	scale parameter of an AL distribution.
p	quantile or skewness parameter, p in (0,1).

Details

Computes the cdf of an AL distribution.

CDF(x) = F(x) = P(X \le x)

where X is a random variable that follows AL(\mu, \sigma, p)

Value

Returns the cumulative probability value at point “x”.

References

Rahman, M. A. (2016). “Bayesian Quantile Regression for Ordinal Models.” Bayesian Analysis, 11(1): 1-24. DOI: 10.1214/15-BA939

Yu, K., and Zhang, J. (2005). “A Three-Parameter Asymmetric Laplace Distribution.” Communications in Statistics - Theory and Methods, 34(9-10), 1867-1879. DOI: 10.1080/03610920500199018

See Also

cumulative distribution function, asymmetric Laplace distribution

Examples

set.seed(101)
x <- -0.5428573
mu <- 0.5
sigma <- 1
p <- 0.25
output <- alcdf(x, mu, sigma, p)

# output
#   0.1143562

bqror documentation built on May 31, 2023, 5:19 p.m.