Description Usage Arguments Value References Examples

Density, cumulative distribution function, quantile function and random sample generation from the generalized tick-exponential family (GTEF) of densities discusse in Gijbels et al. (2019b).

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

`eta` |
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. |

`g` |
This is the "link" function. The function |

`beta` |
This is a vector of probabilities. |

`lower` |
This is the lower limit of the domain (support of the random variable) |

`upper` |
This is the upper limit of the domain (support of the random variable) |

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

`dGTEF`

provides the density, `pGTEF`

provides the cumulative distribution function, `qGTEF`

provides the quantile function, and `rGTEF`

generates a random sample from the generalized tick-exponential family of densities.
The length of the result is determined by *n* for `rGTEF`

, and is the maximum of the lengths of the numerical arguments for the other functions.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
# For identiy link function
y=rnorm(100)
g_id<-function(y){y}
dGTEF(y,eta=0,phi=1,alpha=0.5,p=2,g=g_id)
# cumulative distribution function
pGTEF(q=y,eta=10,phi=1,alpha=0.5,p=2,g=g_id)
# Quantile function
beta=c(0.25,0.5,0.75)
qGTEF(beta=beta,eta=10,phi=1,alpha=0.5,p=2,g=g_id)
# random sample generation
rGTEF(n=100,eta=10,phi=1,alpha=.5,p=2,g=g_id,lower = -Inf, upper = Inf)
# For log link function
y=rexp(100)
g_log<-function(y){log(y)}
dGTEF(y,eta=10,phi=1,alpha=0.5,p=2,g=g_log)
# cumulative distribution function
pGTEF(q=y,eta=10,phi=1,alpha=0.5,p=2,g=g_log)
# Quantile function
g_log<-function(y){log(y)}
#' beta=c(0.25,0.5,0.75)
qGTEF(beta=beta,eta=10,phi=1,alpha=0.5,p=2,g=g_log,lower = 0, upper = Inf)
# random sample generation
rGTEF(n=100,eta=10,phi=1,alpha=.5,p=2,g=g_log,lower = 0, upper = Inf)
``` |

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