Description Usage Arguments Value References Examples

The log-likelihood function *\ell_n(μ,φ,α)=\ln[L_n(μ,φ,α)]*
and parameter estimation of * θ=(μ,φ,α)* in the three parameter quantile-based asymmetric family of densities
by using the maximum likelihood estimation are discussed in Section 3.2 of Gijbels et al. (2019a).

1 |

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

`f` |
This is the reference density function |

`alpha` |
This is the index parameter |

The maximum likehood estimate of paramter *θ=(μ,φ,α)* of the quantile-based asymmetric family of densities

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 | ```
# 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)
rnum=rnorm(100)
mleQBAD(rnum,f=f_N)
mleQBAD(rnum,f=f_N,alpha=.5)
# 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)
mleQBAD(rnum,f=f_La)
mleQBAD(rnum,f=f_La,alpha=.5)
``` |

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