Topp-Leone odd log-logistic exponential distribution: Its improved estimators and applications.

Area of Science:

• Statistics
• Probability theory
• Reliability engineering

Background:

• Lifetime data analysis is crucial in various fields.
• Existing statistical models may not capture complex failure patterns.
• There is a need for flexible and accurate lifetime distributions.

Purpose of the Study:

• To introduce a new flexible lifetime distribution: the Topp-Leone odd log-logistic exponential distribution.
• To investigate the statistical and reliability properties of this new distribution.
• To compare its performance against established lifetime models.

Main Methods:

• The proposed distribution's density and hazard rate functions are analyzed.
• Various estimation methods are explored, including Maximum Likelihood and Least Squares.
• Monte Carlo simulations are conducted to assess estimator performance.

Main Results:

• The Topp-Leone odd log-logistic exponential distribution exhibits versatile shapes for density and hazard rates.
• Simulations indicate robust performance of estimation methods for both small and large sample sizes.
• Real-world data analysis confirms the proposed distribution's superiority over existing models.

Conclusions:

• The novel Topp-Leone odd log-logistic exponential distribution provides a valuable addition to lifetime data analysis.
• Its flexibility and demonstrated performance make it suitable for complex reliability scenarios.
• The proposed model offers improved accuracy in modeling real-world failure data.