### A New Family of Distributions Based on the Hypoexponential Distribution with Fitting Reliability Data

#### Abstract

In this paper, a new general family of distributions using the hypoexponential distribution is introduced and studied. A special case of this family is explored in detail, corresponding to a new finite generalized mixture of generalized exponential distributions. Some of their mathematical properties are provided. We investigate maximum likelihood estimation of the model parameters. Two real data sets are used to prove the potential of this distribution among some recent extensions of the exponential distribution.

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DOI: 10.6092/issn.1973-2201/8260