Abstract
For proper actualization of the phenomenon contained in some lifetime data sets, a generalization, extension or modification of classical distributions is required. In this paper, we introduce a new generalization of exponential distribution, called the generalized odd generalized exponential-exponential distribution. The proposed distribution can model lifetime data with different failure rates, including the increasing, decreasing, unimodal, bathtub, and decreasing-increasing-decreasing failure rates. Various properties of the model such as quantile function, moment, mean deviations, Renyi entropy, and order statistics. We provide an approximation for the values of the mean, variance, skewness, kurtosis, and mean deviations using Monte Carlo simulation experiments. Estimating of the distribution parameters is performed using the maximum likelihood method, and Monte Carlo simulation experiments is used to assess the estimation method. The method of maximum likelihood is shown to provide a promising parameter estimates, and hence can be adopted in practice for estimating the parameters of the distribution. An application to real and simulated datasets indicated that the new model is superior to the fits than the other compared distributions
Highlights
Many classical probability distributions have been used to make inferences about a population based on a set of data from the population
The distribution has monotone and non-monotone failure rate (FR), which allows it to provides a good fit when fitted to a real-life data set. (Abba & Singh, 2018), proposed a three-parameters new odd generalized exponential-exponential (NOGE-E) distribution and studied some of the distributional properties, including the quantile function, moments, moment generating function, entropy and order statistics
Applications we evaluated the fitness of the generalized odd generalized exponential-exponential (GOGE-E) distribution using two real datasets with other known distributions including exponential (E), odd generalized exponential-exponential (OGE-E) and new odd generalized exponential-exponential (NOGE-E) distributions
Summary
Many classical probability distributions have been used to make inferences about a population based on a set of data from the population. The model is constructed using a two-parameters generalized odd generalized exponential (GOGE-G) family of distribution introduced by (Alizadeh et al, 2017) This family of distributions (generator), has a wide advantage, as flexible distributions can be defined with both monotone and nonmonotone FR, even though the baseline FR may be monotonic or constant. The plots reveal the potential of the new model, that, it can be used to models lifetime data with distinct FR shapes, including the decreasing, increasing, bathtub, up-side-down bathtub (unimodal), and decreasing-increasing-decreasing shapes This is important as most of generalizations (modifications or extensions) of the classical lifetime distributions have only the bathtub or unimodal FR shapes, which limits their ability to provide a better fit in modelling some problems with different FR shapes. We can determine the first four moments (for kurtosis ( ) using some known results
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