On log-bimodal alpha-power distributions with application to nickel contents and erosion data

Abstract

In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes.