Chen Exponential Distribution with Applications to Engineering Data
Abstract
We have established a new modification of the Chen distribution and named it the Chen exponential distribution. The explicit expressions for the mean past lifetime function, quantile function, mode, moments and conditional moments, skewness, kurtosis, and the density function for the order statistics are derived, and the distribution of the minimum, maximum, and median of order statistics are also obtained. The parameters of the new distribution are estimated by applying the least squares, Cramer-von Mises, and maximum likelihood estimation methods. We also derive and calculate the information matrix for maximum likelihood estimates. In addition, a simulation study is conducted to investigate the behavior of the maximum likelihood estimates. To assess the potential of the proposed model, two real-world data sets are used. The R software is used to perform graphical and numerical computations. To judge the performance of the model, model selection criteria and goodness-of-fit tests are performed. From the findings and outcomes, it has been observed that the new model performs better than some competing models taken for comparison. We expect that the suggested model will be an alternative model in the fields of engineering, life sciences, medicine, theory of probability distribution, and statistics.
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