On the exponent power sine Lomax distribution with applications in the music education and radiation fields

Considering the decisive role of probability distributions in applied fields, we consider and implement a new probability distribution. The proposed distribution is a sine-oriented modification of the Lomax distribution by modifying the power Lomax distribution, and is called the exponent sine power Lomax (ESP-Lomax) distribution. We go into the computation of the mathematical properties and analytical studies based on these properties of the ESP-Lomax distribution. In addition, this paper also provides the mathematical derivation of the heavy-tailed characteristics of the ESP-Lomax distribution. The mathematical computation of maximum likelihood estimators and simulation studies under various parameter settings based on the ESP-Lomax distribution is also provided. In comparison with other distributions, we check and establish the practical superiority of the ESP-Lomax distribution using two practical data sets, which are sourced from two different applied sectors. By employing several key tools, we empirically demonstrated that the ESP-Lomax distribution can fit real-world events well across various domains.