Description Usage Arguments Value References Examples

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

1 | ```
LogLikGAD(y, eta, phi, alpha, f, g)
``` |

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

`eta` |
This is the location parameter |

`phi` |
This is the scale parameter |

`alpha` |
This is the index parameter |

`f` |
This is the reference density function |

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

`LogLikGAD`

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

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 | ```
# 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)
g_id<-function(y){y}
g_log<-function(y){log(y)}
LogLikGAD(y,eta=0,phi=1,alpha=0.5,f=f_N,g=g_id) # For identity-link
LogLikGAD(rexp(100,0.1),eta=10,phi=1,alpha=0.5,f=f_N,g=g_log) # For log-link
# 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)
LogLikGAD(y,eta=0,phi=1,alpha=0.5,f=f_La,g=g_id) # For identity-link
LogLikGAD(rexp(100,0.1),eta=10,phi=1,alpha=0.5,f=f_La,g=g_log) # For log-link
``` |

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