Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The need for flexible probability distributions in modeling complex data.
• Limitations of existing distributions in capturing diverse hazard rate behaviors.

Purpose of the Study:

• Introduce and characterize the two-parameter exponentiated Teissier distribution.
• Investigate its properties, including hazard rate shapes and reliability measures.
• Develop and compare parameter estimation techniques.

Main Methods:

• Derivation of moments, quantiles, and entropy.
• Analysis of stress-strength reliability and stochastic orderings.
• Development of estimators: likelihood, least squares, weighted least squares, and product spacings.
• Algorithm for random variate generation.
• Simulation studies for performance comparison.

Main Results:

• The exponentiated Teissier distribution exhibits increasing, decreasing, and bathtub-shaped hazard rates.
• Novel estimators for the distribution's parameters were developed and evaluated.
• The distribution demonstrated good performance when fitted to real data sets.

Conclusions:

• The proposed distribution is a valuable addition to the statistical toolkit for reliability and survival analysis.
• The developed estimation methods provide robust approaches for parameter estimation.
• The flexibility of the distribution allows for modeling a wider range of data patterns.