Abstract
In this paper a new two-parameter distribution is proposed. This new model provides more flexibility to modeling data with increasing and bathtub hazard rate function. Several statistical and reliability properties of the proposed model are also presented in this paper, such as moments, moment generating function, order statistics and stress-strength reliability. The maximum likelihood estimators for the parameters are discussed as well as a bias corrective approach based on bootstrap techniques. A numerical simulation is carried out to examine the bias and the mean square error of the proposed estimators. Finally, an application using a real data set is presented to illustrate our model.
Highlights
Mixture models have been playing an important role in distribution theory (Patil and Rao, 1978)
A simple case can be considered where new models are generated by a two-component mixture f (t|Λ1, Λ2, p) = pf1(t|Λ1) + (1 − p)f2(t|Λ2), (1)
Where 0 ≤ p ≤ 1 is mixing proportion (MP) and Λ1, Λ2 are the parameters related to the probability density function (PDF) f1(·) and f2(·)
Summary
Mixture models have been playing an important role in distribution theory (Patil and Rao, 1978). Ramos and Louzada (2019) proposed a new one parameter distribution based on the mixture of a gamma and an exponential distribution. Ghitany et al (2011) proposed a weighted Lindley model based on the mixture of two gamma distribution, where the MP is p = θ/(λ + θ), λ > 0 and θ > 0. Ramos and Louzada (2016) unified these models by considering the mixture of two generalized gamma distributions. For the new distribution the hazard function has increasing or bathtub shape, depending on the values of the parameters This property plays an important role to describe lifetime data (Chen, 2000; Wang et al, 2002).
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