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.