Description Usage Arguments Value References Examples

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).

1 2 3 4 5 6 7 |

`y, q` |
These are each a vector of quantiles. |

`mu` |
This is the location parameter |

`phi` |
This is the scale parameter |

`alpha` |
This is the index parameter |

`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. |

`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.

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.

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)
``` |

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