Efficient estimation of Pareto model: Some modified percentile estimators

Area of Science:

• Statistics
• Probability Theory
• Econometrics

Background:

• Pareto distribution is widely used in various fields.
• Accurate parameter estimation is crucial for reliable analysis.
• Traditional percentile estimators may have limitations.

Purpose of the Study:

• To propose and evaluate novel modified percentile estimators for Pareto distribution parameters.
• To compare the performance of these new estimators against traditional ones.
• To identify the most efficient and precise estimation method.

Main Methods:

• Development of three modified percentile estimators based on median, geometric mean, and expectation of the empirical cumulative distribution function of the first-order statistic.
• Monte Carlo simulation to assess estimator performance under various parameter combinations and sample sizes.
• Evaluation using total mean square error and total relative deviation metrics.

Main Results:

• The modified percentile estimator based on the expectation of the empirical cumulative distribution function of the first-order statistic showed superior performance.
• This estimator provided more efficient and precise parameter estimates compared to other considered methods.
• Simulation findings were validated using two real-life examples, including comparisons with maximum likelihood and moment estimators.

Conclusions:

• Modified percentile estimators offer improved parameter estimation for the Pareto distribution.
• The expectation-based modified estimator is recommended for its enhanced accuracy and precision.
• The findings have practical implications for applications relying on Pareto distribution modeling.