Description Usage Arguments Value References See Also Examples

Density, cumulative distribution function, quantile function and random sample generation
from the quantile-based asymmetric Student's-*t* distribution (ATD) proposed in Gijbels et al. (2019a).

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 |

`nu` |
This is the degrees of freedom parameter |

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

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

`dATD`

provides the density, `pATD`

provides the cumulative distribution function, `qATD`

provides the quantile function, and `rATD`

generates a random sample from the quantile-based asymmetric Student's-*t* distribution.
The length of the result is determined by *n* for `rATD`

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

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# Quantile-based asymmetric Student's-\eqn{t} distribution (ATD)
# Density
rnum<-rnorm(100)
dATD(rnum,mu=0,phi=1,alpha=0.5,nu=10)
# Distribution function
pATD(rnum,mu=0,phi=1,alpha=0.5,nu=10)
# Quantile function
beta<-c(0.25,0.5,0.75)
qATD(beta=beta,mu=0,phi=1,alpha=.5,nu=10)
# random sample generation
rATD(n=100,mu=0,phi=1,alpha=.5,nu=10)
``` |

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