Analysis, inference, and application of Unit Haq distribution to engineering data

Abstract

Modeling datasets with constraints inside the unit interval may be done well with common continuous distributions such as the Beta and Kumaraswamy. In this study, a new one-parameter Unit Haq (UH) distribution is introduced to analyze more complex datasets. Some Key mathematical properties for the UH distribution including moments, and incomplete moments have been derived. Reliability characteristics including hazard function, mean residual life function, stochastic ordering, and Rényi entropy are also derived. Various parameter estimation methods are discussed and evaluated through Monte Carlo simulations. Applications of the UH distribution are demonstrated using engineering datasets, highlighting its superior fit compared to established distributions. The model parameter is also estimated using the Bayesian approach.

Keywords

• Unit Haq distribution
• Moments
• Reliability characteristics
• Inference
• Analysis