Development of a new statistical distribution with insights into mathematical properties and applications in industrial data in KSA

This study presents the development of a novel distribution through a transformation involving error functions, namely the error function inverse Weibull model, along with an overview of the fundamental characteristics of the proposed model. The hazard function of the recommended model is very flexible; it fits increasing, decreasing, and unimodal factors. For estimating the unknown parameters, we suggested two estimation methods, including the maximum likelihood estimation and Bayesian techniques. We perform a Monte Carlo simulation analysis to assess the stability of the parameter estimation procedure. The numerical results of these simulations show that the Bayesian technique under the square error loss function performs better than another method to obtain the model parameters. We thoroughly examine the significance of the proposed model and illustrate its application using three real-world data sets from the industrial sector. We compared the suitability and flexibility of the suggested distribution with several others, and the results showed that it fits the real-world data better than the competing models.