A novel probabilistic model with properties: Its implementation to the vocal music and reliability products

Abstract

So far in the literature, numerous probabilistic models and families of probabilistic models have been suggested and put into practice. A large portion of these probabilistic models are developed and updated by introducing new parameters ranging up to five. There are only a few methods that are introduced without adding additional parameters. This paper also contributed to the development of a probabilistic model without adding additional parameters. The proposed model is introduced by incorporating the weighted distributional strategy and the weighted Ramos–Louzada distribution. Therefore, the generalized weighted Ramos–Louzada distribution is a suitable name for the newly proposed model. The derivation of the estimators based on the maximum likelihood for this novel model is presented. Certain distributional properties of the generalized weighted Ramos–Louzada distribution are derived. In order to validate the effectiveness and superiority of the generalized weighted Ramos–Louzada distribution, three applications are chosen as examples. The first two applications are considered from the physical sciences, while, the third application is taken from the musical area. We consider four statistical tests to show the validatity of the proposed model over some well-known established models. The findings from the statistical tests consistently indicate that the proposed model performs better than its rivals.

Keywords

• Weighted distribution
• Identifiability characteristics
• Distributional properties
• Simulation
• Vocal music
• Physical sciences