A novel probabilistic model: Simulation and modeling the time duration in musical education and engineering

Statistical analysis of the time-to-event scenarios commonly involves the use of the exponential and Rayleigh distributions. However, the exponential distribution is constrained by its constant failure rate, while the Rayleigh distribution exhibits a growing (or increasing) failure rate. The linear failure rate distribution provides a broader perspective by encompassing both of these distributions, including the possibility of a non-increasing hazard function. In this paper, a new distribution is introduced, which could be considered as one of the major modifications to the linear failure rate distribution, known as the weighted linear failure rate distribution. The model proposed illustrates both monotonic and a known non-monotonic failure rate. This paper extensively explores the characteristics of the proposed distribution. It presents the maximum likelihood estimates for the unknown parameters and includes a simulation study. The analysis focuses on three real data sets obtained from the fields of musical education and engineering. By employing three decisive tools, it is observed that the current distribution provides a superior fit in comparison to several other widely recognized distributions.