Abstract. In this paper, a generalization of the exponential integral is given. As a consequence, several inequalities involving the generalized function are derived. Among other analytical techniques, the procedure utilizes the Hölder's and Minkowski's inequalities for integrals.
In this study, a new continuous distribution called the Kumaraswamy Erlang-truncated exponential distribution is introduced and studied. The mathematical properties of the new model such as the quantile function, moments and moment generating function and order statistics are derived. The estimation of the parameters of the model is approached by the method of maximum likelihood. The importance of the model is illustrated by means of application to real data set.
In this paper, we propose a three-parameter probability distribution called equilibrium renewal Burr XII distribution using the equilibrium renewal process. The statistical properties of the distribution such as moment, mean deviation, order statistics, moment generating function, Beforroni and Lorenz curve, survival function, reversed hazard rate and hazard function were derived. The method of maximum likelihood is used for estimating the distribution's parameters and a simulation study is conducted to assess the performance of the parameters. We provide two applications in eld of health to demonstrate the importance of the proposed distribution.
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