Two Weighted Distributions Generated by Exponential Distribution

In this paper, we propose new classes of weighted distributions by incorporating exponential distribution in Azzalini’s method. Resulting weighted models generated by exponential distribution are: the weighted gamma-exponential model and the weighted generalized exponenatial- exponential model. The hazard rate function of these distributions has different shapes including increasing, decreasing and unimodal. The moment properties of the proposed distributions are studied. Maximum likelihood estimators (MLEs) of the unknown parameters cannot be obtained in explicit forms and they have to be obtained by solving some numerical methods. Two data sets have been analyzed for illustrative purposes, which show that the proposed models can be used quite effectively in analyzing real data.