Statistics and Its Interface

Volume 11 (2018)

Number 2

Censored bimodal symmetric-asymmetric families

Pages: 237 – 249

DOI: https://dx.doi.org/10.4310/SII.2018.v11.n2.a3

Authors

Guillermo Martínez-Flórez (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Colombia)

Heleno Bolfarine (Departamento de Estatítica, IME, Universidade de São Paulo, Brazil)

Héctor W. Gómez (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Chile)

Abstract

In this paper, we introduce two new families of distributions that are suitable for fitting unimodal as well as bimodal symmetric and asymmetric censored data. The models extend the skew normal model to bimodal symmetric and asymmetric situations and typically involves less parameters to be estimated than mixtures of normal distributions. Maximum likelihood estimation (MLE) is discussed and Fisher information matrices are derived. Results of a simulation study indicate stable parameter recovery in moderate and large samples. Applications to two real data sets are reported. The first data set is related to results of a study on antiretroviral therapy (HAART) to AIDS patients with strong evidence of bimodality and asymmetry. The second data set (fetal weight of unborn children) presents bimodal symmetry, well captured by the model introduced.

Keywords

bimodal distribution, generalized Gaussian distribution, kurtosis, power-normal model, skew-normal distribution, skewness

Received 25 October 2016

Published 7 March 2018