The Beta Exponentiated Nadarajah-Haghighi Distribution: Theory and Applications

Abdus M Saboor (1) , Muhammad Nauman Khan (1) , Gauss M Cordeiro (2) , Ibrahim M Elbatal (3) , Rodrigo R Pescim (4)

1 Department of Mathematics
2 Departamento de Estatítica
3 Department of Mathematics and Statistics
4 Departamento de Estatítica

We introduce and study the beta exponentiated Nadarajah-Haghighi model, which has increasing, decreasing, upside-down bathtub and bathtub shaped hazard functions. Some of its mathematical properties are determined including a power series for the quantile function. The model parameters are estimated by the method of maximum likelihood. The new distribution and some other competitive models are fitted to a meteorological data set. We prove empirically that it has a superior performance compared with other distributions based on some goodness-of-fit statistics. As a result, some parameters such as return level and mean deviation about the return level are estimated under the best model. We define a new parametric model based on the introduced distribution.

Mots clés: Beta distribution; Moment generating function; Monte Carlo; simulation

Domaines: Mathématiques [math]; Statistiques [stat]

Abdus M Saboor, Muhammad Nauman Khan, Gauss M Cordeiro, Ibrahim M Elbatal, Rodrigo R Pescim. The Beta Exponentiated Nadarajah-Haghighi Distribution: Theory and Applications. Mathematica Slovaca, In press. ⟨hal-01570564⟩