A new heavy-tailed distribution: Its heavy-tailed characteristics with implementations in the radiation and music engineering

Recognizing the significant influence that data analysis tools have in diverse fields, we present an innovative analytical approach to enhance and expand the existing variety of distribution methods. Our work centers on combining the inverse Lomax distribution with a recognized distributional approach, leading to what we call the new heavy-tailed inverse Lomax (NHTI-Lomax) distribution. The NHTI-Lomax distribution is able to capture the key characteristics linked to heavy-tailed distributions. This fact is supported by both visual illustrations and thorough mathematical proof. The identifiability features and the heavy-tailed characteristics of the NHTI-Lomax distribution are thoroughly examined and mathematically verified. Furthermore, we obtain the maximum likelihood estimators relevant to this distribution. Additionally, we conduct an analysis of the NHTI-Lomax distribution’s effectiveness with simulated data, allowing us to assess its practical relevance and performance across different situations. In practical terms, the significance of the NHTI-Lomax distribution is evaluated using perspectives from real-world data. The first application pertains to music engineering. While, the second application focuses on the field of radiation sciences. By employing certain established information criteria, we show that the NHTI-Lomax distribution outperforms certain alternative distributions.