# A novel extension of half-logistic distribution with statistical inference, estimation and applications

## TL;DR

This paper introduces a new statistical distribution that offers flexible hazard rate shapes and performs better than existing models when tested on real data.

## Contribution

The novel OFHL distribution combines the half-logistic and odd Frechet-G families, offering improved flexibility and performance.

## Key findings

- The OFHL model exhibits hazard rate functions with decreasing, increasing, bathtub, and inverted U shapes.
- Six estimation methods were evaluated for the OFHL model through Monte Carlo simulations.
- The OFHL model outperformed existing models in real-world data applications.

## Abstract

In the present study, we develop and investigate the odd Frechet Half-Logistic (OFHL) distribution that was developed by incorporating the half-logistic and odd Frechet-G family. The OFHL model has very adaptable probability functions: decreasing, increasing, bathtub and inverted U shapes are shown for the hazard rate functions, illustrating the model’s capacity for flexibility. A comprehensive account of the mathematical and statistical properties of the proposed model is presented. In estimation viewpoint, six distinct estimation methodologies are used to estimate the unknown parameters of the OFHL model. Furthermore, an extensive Monte Carlo simulation analysis is used to evaluate the effectiveness of these estimators. Finally, two applications to real data are used to demonstrate the versatility of the suggested method, and the comparison is made with the half-logistic and some of its well-known extensions. The actual implementation shows that the suggested model performs better than competing models.