Statistical inference for a general class of distributions with time-varying parameters

Area of Science:

• Probability theory
• Statistical modeling
• Reliability engineering

Background:

• Independent, not necessarily identically distributed random variables are fundamental in statistical analysis.
• Existing distributions may not adequately capture time-varying event data.
• Reliability and survival analysis require robust models for time-to-event phenomena.

Purpose of the Study:

• To introduce a general class of probability distributions closed under minima for independent, not necessarily identically distributed random variables.
• To model time-varying parameters within this distribution class, particularly for reliability and survival analysis.
• To investigate parameter estimation and model selection for these time-varying distributions.

Main Methods:

• Development of a general class of distributions including Geometric, Exponential, Weibull, and Pareto distributions.
• Application of maximum likelihood estimation (MLE) for parameter estimation.
• Analysis of asymptotic properties of the estimators.
• Utilizing classical model selection criteria for competing models.

Main Results:

• The proposed class of distributions accommodates time-varying parameters effectively.
• Maximum likelihood estimators demonstrate desirable asymptotic properties.
• Model selection criteria show performance in identifying the correct time-varying model.

Conclusions:

• The introduced distribution class offers a versatile framework for modeling time-varying data in reliability and survival analysis.
• The developed estimation and model selection procedures provide accurate and reliable methods for practical applications.
• The study validates the utility of the proposed methods through real and simulated data examples.