QBAsyDist (version 0.1.2)

AEPD: Quantile-based asymmetric exponential power distribution

Description

Density, cumulative distribution function, quantile function and random sample generation from the quantile-based asymmetric exponential power distribution (AEPD) studied in Gijbels et al. (2019b). An alternative form of the density AEPD is also studied in Komunjer (2007).

Usage

dAEPD(y, mu, phi, alpha, p)
pAEPD(q, mu, phi, alpha, p)
qAEPD(beta, mu, phi, alpha, p)
rAEPD(n, mu, phi, alpha, p)

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 \(\alpha\).

p

This is the shape parameter, which must be positive.

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

dAEPD provides the density, pAEPD provides the cumulative distribution function, qAEPD provides the quantile function, and rAEPD generates a random sample from the quantile-based asymmetric exponential power distribution.

References

Gijbels, I., Karim, R. and Verhasselt, A. (2019b). Quantile estimation in a generalized asymmetric distributional setting. To appear in Springer Proceedings in Mathematics & Statistics, Proceedings of `SMSA 2019', the 14th Workshop on Stochastic Models, Statistics and their Application, Dresden, Germany, in March 6--8, 2019. Editors: Ansgar Steland, Ewaryst Rafajlowicz, Ostap Okhrin.

Komunjer, I., (2007). Asymmetric power distribution: theory and applications to risk measurement. Journal of Applied Econometrics, 22(5), 891-921.

Examples

# NOT RUN {
# Quantile-based asymmetric exponential power distribution
# Density
rnum<-rnorm(100)
dAEPD(y=rnum,mu=0,phi=1,alpha=.5,p=2)

# Distribution function
pAEPD(q=rnum,mu=0,phi=1,alpha=.5,p=2)

# Quantile function
beta<-c(0.25,0.5,0.75)
qAEPD(beta=beta,mu=0,phi=1,alpha=.5,p=2)

# random sample generation
rAEPD(n=100,mu=0,phi=1,alpha=.5,p=2)

# }