Abstract
In this work, a new lifetime model is introduced and studied. The major justification for the practicality of the new model is based on the wider use of the exponentiated Weibull and Weibull models. We are also motivated to introduce the new lifetime model since it exhibits decreasing, upside down-increasing, constant, increasing-constant and J shaped hazard rates also the density of the new distribution exhibits various important shapes. The new model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be considered as a suitable model for fitting the symmetric, left skewed, right skewed and unimodal data. The importance and flexibility of the new model is illustrated by four read data applications.
Highlights
In modeling cancer patient's data, the new model is much better than the transmuted linear exponential, Weibull, Transmuted modified-Weibull, modified beta-Weibull, transmuted additive-Weibull, exponentiated transmuted generalized Rayleigh models
We prove empirically the great importance and wide flexibility of the Burr-Hatke exponentiated Weibull (BHEW) model in modeling four types of lifetime data, the new model provides adequate fits as compared to other Weibull models with small values for W* and A* so the new model is much better than other competitive model in modeling four data sets
The proposed lifetime model is much better than the Poisson Topp Leone-Weibull, Marshall Olkin extended-Weibull, Gamma-Weibull, Kumaraswamy-Weibull, Weibull-Fréchet, B-W, Beta-Weibull, Kumaraswamy transmuted-Weibull, transmuted modified-Weibull, transmuted exponentiated generalized Weibull, modified beta-Weibull and McDonald-Weibull models in modeling the failure times data
Summary
The Burr-Hatke differential equation (B.H.D.E.) can be written as dF/dt = g(t, F)F(1 − F) with F0 = F(t0)|[t0∈R],. Using (1), Maniu and Voda (2008) introduced and studied the BH distribution with C.D.F. and P.D.F. given by (t + 1)−1. By replacing t by {− log[GEW(x)]}, Yousof et al, (2018) introduced a new flexible family of distributions called the BH-G family of distributions. {⏞1 − [1 − exp(−xβ)]α}θ Fθ,α,β(x) = 1 − 1⏟− log{1 − [1 − exp(−xβ)]α}. The P.D.F. corresponding to (2) is given by fθ,α,β(x) = f(x ; θ , α, β) = αβxβ−1 exp(−xβ) [1 − exp(−xβ)]α−1. × [θ(1 − log{1 − [1 − exp(−xβ)]α}) + 1]. The R.F. and hazard rate function (H.R.F.) of new model are given by {1 − [1 − exp(−xβ)]α}θ. Some useful extension of the W and EW models are developed by Yousof et al, (2015), Aryal et al (2017), Yousof et al, (2017), Brito et al, (2017), Hamedani et al, (2017), Aboraya (2018), Almamy et al, (2018), Cordeiro et al, (2018), Korkmaz et al, (2019), among others
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