AEPD: Quantile-based asymmetric exponential power distribution

Description Usage Arguments Value References Examples

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

1
2
3
4
5
6
7
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 μ.

phi

This is the scale parameter φ.

alpha

This is the index parameter α.

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
# 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)

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

Related to AEPD in QBAsyDist...