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Problem statement: Actuarial science has grown much popularity in the recent years due to the growth of insurance companies. In practice, the data involved in actuarial science are mostly counts which may be over-,equi-or under-dispersed. Many probability distributions were proposed to model such data such as the mixed Poisson distributions. However, the estimation methodologies based on such mixed Poisson distributions may be complicated and may not yield consistent and efficient estimates.doi:10.3844/jmssp.2010.92.95 fatcat:pgvzky6v7zaanhlvybyrd5bibq