An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Pareto distribution is widely applied in reliability, survival analysis, and financial studies.
• Modeling heterogeneous populations requires specialized statistical distributions.
• Mixture models are effective for representing subpopulations with distinct characteristics.

Purpose of the Study:

• To develop a Pareto mixture distribution model for a heterogeneous population composed of two subgroups.
• To derive Bayes estimators for the distinct shape and scale parameters of each subgroup using squared error loss function.
• To calculate standard errors for the derived Bayes estimators.

Main Methods:

• Utilized a Pareto mixture distribution to model a two-subgroup heterogeneous population.
• Derived Bayes estimators employing both flat and conjugate priors.
• Calculated standard errors for the Bayes estimators.
• Computed components of the Fisher Information matrix.

Main Results:

• Successfully derived Bayes estimators for shape and scale parameters under different prior assumptions.
• Provided standard errors for assessing the precision of these estimators.
• Developed components of the Fisher Information matrix, valuable for further statistical inference.

Conclusions:

• The proposed Pareto mixture model effectively handles population heterogeneity.
• The derived Bayes estimators offer a robust approach for parameter estimation in such models.
• The inclusion of Fisher Information matrix components enhances the utility of the study for future research in reliability and financial analysis.