Survival analysis based on an enhanced Rayleigh-inverted Weibull model.

Area of Science:

• Statistics
• Reliability Engineering
• Probability Theory

Background:

• Survival models are crucial for analyzing time-to-event data in various fields.
• Existing distributions may not adequately capture complex failure patterns.
• The Kavya-Manoharan transformation offers a flexible framework for developing new statistical distributions.

Purpose of the Study:

• To introduce and analyze a novel two-parameter survival model: the Kavya-Manoharan-Rayleigh inverted Weibull distribution (KMRIWD).
• To investigate the statistical properties and reliability measures of the proposed KMRIWD.
• To evaluate the performance of parameter estimation techniques for the KMRIWD.

Main Methods:

• Development of the KMRIWD by combining the Kavya-Manoharan transformation and the Rayleigh inverted Weibull distribution.
• Analysis of key statistical properties and reliability functions.
• Parameter estimation using the maximum likelihood method and various sampling strategies.
• Performance evaluation through Monte Carlo simulations.
• Comparative analysis with existing survival models using real-world datasets.

Main Results:

• The KMRIWD is defined and its fundamental statistical and reliability characteristics are derived.
• Maximum likelihood estimators for KMRIWD parameters are obtained.
• Monte Carlo simulations demonstrate the effectiveness of the estimation methods.
• Empirical analysis confirms the superior fit of the KMRIWD over competing models on real data.

Conclusions:

• The proposed KMRIWD is a flexible and effective survival model.
• The KMRIWD demonstrates superior performance in fitting real-world reliability data.
• This new distribution offers a valuable tool for reliability analysis and related statistical modeling.