Abstract
The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accommodates symmetrical, right-skewed, left-skewed, reversed-J-shaped, and J-shaped densities and increasing, unimodal, decreasing, reversed-J-shaped, and J-shaped hazard rates. We derive some mathematical properties of the proposed model. The model parameters were estimated using five estimation methods including the maximum likelihood, Anderson–Darling, least-squares, Cramér–von Mises, and weighted least-squares estimation methods. The performance of these estimation methods was assessed by a detailed simulation study. Furthermore, the flexibility of the introduced model was studied using an insurance real dataset, showing that the proposed model can be used to fit the insurance data as compared with twelve competing models.
Highlights
Reliability and survival analysis has several applications, as an important branch of statistics, in different applied fields, such as actuarial science, engineering, demography, biomedical studies, and industrial reliability
The main aim of this paper is to study a new extension of the logistic exponential model based on the inverse power transformation and derive some of its distributional properties
We explore the estimation of the inverse power logistic exponential (IPLE) parameters by different methods of estimation including the maximum likelihood estimators (MLEs), Anderson–Darling estimators (ADEs), least-squares estimators (LSEs), Cramér–von Mises estimators (CVMEs), and weighted least-squares estimators (WLSEs)
Summary
Reliability and survival analysis has several applications, as an important branch of statistics, in different applied fields, such as actuarial science, engineering, demography, biomedical studies, and industrial reliability. Several lifetime distributions have been proposed in the statistical literature to model data in many applied sciences. The exponential distribution is used in modeling real-life data due to its lack of memory property, and it is analytically tractable. Its applicability was limited because it has only a constant hazard rate and decreasing density function. Many researcher have been interested in proposing modified forms of the exponential distribution to increase its flexibility. Some recent extensions of the exponential distribution include the exponentiated exponential [1], beta exponential [2], beta generalized exponential [3], transmuted generalized exponential [4], Harris extended exponential [5], Kumaraswamy transmuted exponential [6], Marshall–Olkin Nadarajah–Haghighi [7], modified exponential [8], alpha power exponential [9,10], odd exponentiated half-logistic exponential [11], Marshall–Olkin logistic exponential [12], generalized odd log-logistic exponential [13], Marshall–Olkin alpha power exponential [14], extended odd Weibull exponential [15], odd inverse Pareto exponential [16], modified Kies exponential [17], Topp–Leone moment exponential [18], heavy-tailed exponential [19], and odd log-logistic Lindley exponential distributions [20]
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