Inference for compound truncated Poisson log-normal model with application to maximum precipitation data

The main objective of this paper is to propose a new general family of distributions, namely compound truncated Poisson log-normal distribution of which log-normal distribution is a special case. The proposed model has three unknown parameters, and it can take variety of shapes. It can be used effectively in analyzing maximum precipitation data during a particular period of time obtained from different stations. It is assumed that the number of stations operate follows a zero-truncated Poisson random variables, and the daily precipitation follows a log-normal random variable. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals can also be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model it is observed that the proposed model provides better fit than some of the existing models.