Abstract
An extension of the cosine generalized family is presented in this paper by using the cosine trigonometric function and method of parameter induction concurrently. Prominent characteristics of the proposed family along with useful results are extracted. Moreover, two new subfamilies and several special models are also deduced. A four-parameter model called an Extended Cosine Weibull (ECW) with its mathematical properties is studied deeply. Graphical study reveals that the new model adopts right- and left-skewed, symmetrical, and reversed-J density shapes, while all possible monotone and nonmonotone shapes are exhibited by the hazard rate function. The maximum likelihood technique is exercised for parametric estimation, while estimation performance is accessed via Monte Carlo simulation study graphically and numerically. The superiority of the presented model over several outstanding and competing models is confirmed via three reliability and survival dataset applications.
Highlights
Introduction withMotivations is twenty-first century started with setting up and broadening new graphing and analytical instruments for current modern statistics
An immense research work about the theory and applications of statistical distributions exists in the literature. e first reason is the thrust of statisticians to develop novel and flexible models possessing significant mathematical and graphical characteristics. e struggle, challenging, and endless work of statisticians bore fruit, and many modified, extended, and generalized families of distributions are introduced; for more information, see [2–4]. e literature review explores the second reason that simple and nongeneralized models provide an inadequate fit compared to extended and generalized models, especially in real-life situations. e third and very important fact is that the data behave in a more complex way than what is commonly expected in many disciplines
The reader is referred to the memorable contribution [5] about the transformed- (T-) transformer (X) mechanism of developing new families of statistical distributions, extended work [6] regarding the McDonald-G family, and pivotal work on exponentiated generalized families [7]
Summary
E hazard rate function (hrf ) h(x), survival function (sf ) S(x), reversed hazard rate function (rhrf ) r(x), cumulative hazard rate function (chrf ) H(x), mills’ ratio m(x), conditional reliability function G(G(x), α, β|t), and elasticity e(x) are, respectively, given under π/2αβg(x)G(x)α− 1 sin π/2G(x)α1 − cos π/2G(x)αβ− 1 h(x). 1 − 1 − cos π/2G(x + t)αβ G(G(x), α, β|t) 1 − 1 − cos π/2G(t)αβ , e(x) z ln1 − cosπ G(x)αβ. Quantile function [32] Better GoF and flexibility [33] Hjorth’s IDB generator [34]. Parameters (α, β) (θ, α, β) (λ, α, β) (σ, λ, α, β) (s, c, k, α, β) (s, μ, α, β) (σ, μ, α, β) (σ, μ, α, β)
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