QBAsyDist (version 0.1.2)

ALaD: Quantile-based asymmetric Laplace distribution

Description

Density, cumulative distribution function, quantile function and random sample generation for the quantile-based asymmetric Laplace distribution (ALaD) discussed in Yu and Zhang (2005) and Gijbels et al. (2019a).

Usage

dALaD(y, mu, phi, alpha)
pALaD(q, mu, phi, alpha)
qALaD(beta, mu, phi, alpha)
rALaD(n, mu, phi, alpha)

Arguments

y, q

These are each a vector of quantiles.

mu

This is the location parameter \(\mu\).

phi

This is the scale parameter \(\phi\).

alpha

This is the index parameter \(\alpha\).

beta

This is a vector of probabilities.

n

This is the number of observations, which must be a positive integer that has length 1.

Value

dALaD provides the density, pALaD provides the cumulative distribution function, qALaD provides the quantile function, and rALaD generates a random sample from the quantile-based asymmetric Laplace distribution. The length of the result is determined by \(n\) for rALaD, and is the maximum of the lengths of the numerical arguments for the other functions.

References

Gijbels, I., Karim, R. and Verhasselt, A. (2019a). On quantile-based asymmetric family of distributions: properties and inference. International Statistical Review, https://doi.org/10.1111/insr.12324.

Yu., K, and Zhang, J. (2005). A three-parameter asymmetric Laplace distribution and its extension. Communications in Statistics<U+2013>Theory and Methods, 34(9-10), 1867<U+2013>1879.

See Also

dQBAD, pQBAD, qQBAD, rQBAD

Examples

# NOT RUN {
# Density
rnum<-rnorm(100)
dALaD(y=rnum,mu=0,phi=1,alpha=.5)

# Distribution function
 pALaD(q=rnum,mu=0,phi=1,alpha=.5)

# Quantile function
beta<-c(0.25,0.5,0.75)
qALaD(beta=beta,mu=0,phi=1,alpha=.5)

# random sample generation
rALaD(n=100,mu=0,phi=1,alpha=.5)


# }