Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt. E-mail:
The aim of this paper is to introduce a random sum of a new type of mixtures of distributions by taking the discrete parameters has a continuous distribution. The random sum of Erlang-truncated exponential mixture (mixture of Erlang distribution when the mixing distribution is a single left truncated exponential distribution), and random sum binomial-exponential mixture are derived. Also the parameters in Erlang-truncated exponential mixture and binomial-exponential mixture are estimated by using maximum likelihood estimator (MLE) method.
Mixtures of distributions, Random sum: Truncated distributions, Failure rate functions, Maximum likelihood estimator
