Weibull-Normal Distribution and its Applications

Abstract

In this paper, a Weibull-normal distribution, based on the standard quantile function of log-logistic distribution, is defined and studied. Some properties of the probability distribution are discussed. The Weibull-normal distribution is found to be unimodal or bimodal. The distribution can be right skewed or left skewed. The method of maximum likelihood estimation is suggested to estimate the parameters of the distribution. Three numerical data sets are used to illustrate the applications of the Weibullnormal distribution.

Keywords

• T-R{Y}framework
• Bimodal
• Hazard function
• Estimation