ALaD: Quantile-based asymmetric Laplace distribution

Description Usage Arguments Value References See Also Examples

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

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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 μ.

phi

This is the scale parameter φ.

alpha

This is the index parameter α.

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–Theory and Methods, 34(9-10), 1867–1879.

See Also

dQBAD, pQBAD, qQBAD, rQBAD

Examples

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# 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)

QBAsyDist documentation built on Sept. 4, 2019, 1:05 a.m.

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