Description Usage Arguments Value References Examples

Log-Likelihood function *\ell_n(μ,φ,α)=\ln[L_n(μ,φ,α)]*
in the three parameter quantile-based asymmetric family of densities defined in Section 3.2 of Gijbels et al. (2019a).

1 | ```
LogLikQBAD(y, mu, phi, alpha, f)
``` |

`y` |
This is a vector of quantiles. |

`mu` |
This is the location parameter |

`phi` |
This is the scale parameter |

`alpha` |
This is the index parameter |

`f` |
This is the reference density function |

`LogLikQBAD`

provides the realized value of the Log-likelihood function of quantile-based asymmetric family of distributions.

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 | ```
# Example 1: Let F be a standard normal cumulative distribution function then
f_N<-function(s){dnorm(s, mean = 0,sd = 1)} # density function of N(0,1)
y<-rnorm(100)
LogLikQBAD(y,mu=0,phi=1,alpha=0.5,f=f_N)
# Example 2: Let F be a standard Laplace cumulative distribution function then
f_La<-function(s){0.5*exp(-abs(s))} # density function of Laplace(0,1)
LogLikQBAD(y,mu=0,phi=1,alpha=0.5,f=f_La)
``` |

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