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Abstract We propose a new Nadarajah-Haghighi (NH) distribution by applying the record transmutation function to the NH distribution for enhanced flexibility in data modeling. We discuss the shape of the probability density function and hazard function. Furthermore, we obtain quantile function, moments and moment generating function of the distribution. Moreover, we study various estimators for the parameters, such as maximum likelihood estimators, ordinary least squares and weighted least squares estimators, Anderson-Darling estimators, and Cram´er-von Mises estimators. The biases and mean squared errors of these estimators are thoroughly examined through Monte Carlo simulation studies. To demonstrate the practical application of the proposed distribution, two real data analysis are considered. The results highlight the effectiveness of the proposed distribution in modeling real-life data, with the model exhibiting superior fitting performance compared to other competing models.
Kumar et al. (Tue,) studied this question.