In probability theory, the mixture distribution M has a density function M ( ) i I i Xi ( ) f t w f t ∈ = Σ for the collection of random variables , i X i∈I ⊂ and weighted by 0 i w ≥ and 1 i I i w ∈ Σ = . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by i w ∈ , and maintaining 1 i I i w ∈ Σ = . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.
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