Abstract
In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient's survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov–Smirnov (KS) algorithm for fitting Type-I censored data.
Highlights
Modeling real-life events and natural processes using probability distributions is one of the most important processes in statistics and probability, where these processes are characterised by complexity and risk
In order to compare between a large number of distributions, we must base such a comparison on certain criteria: one of these information criteria is called the Akaike information criterion (AIC) though there are other criteria which are called the Bayesian information criterion (BIC), and we can refer to the Hannan–Quinn criterion (for more information on the criterion (HQIC), see Hannan and Quinn [42]), and for more information and last criteria called the consistent Akaike information criterion (CAIC), refer to the study by Bozdogan [43]; all these criteria were used to determine which model among all competing ones is the best for statistical modeling of the data
Simulations were performed to test the efficiency of the estimation methods. e MH algorithm has a great role for obtaining an approximation for the Bayesian estimates
Summary
Modeling real-life events and natural processes using probability distributions is one of the most important processes in statistics and probability, where these processes are characterised by complexity and risk. A superior novel family of distribution dubbed as a new exponential-X (NEX) family was introduced by Huo et al [11]. A new lifetime distribution called the Weibull Frechet distribution, which has four parameters, has been defined and studied by Afify et al [15]. E innovations and encouragements to write this article are to introduce a new exponential-X Frechet distribution as a good fit for the lifetime models that have increasing, decreasing, and bathtub failure rates.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
