Confidence interval estimation for the difference of censored zero-inflated gamma distributions

Area of Science:

• Statistics
• Biostatistics
• Environmental Science

Background:

• Accurate statistical inference is crucial for analyzing complex data.
• Zero-inflated gamma distributions with censored data present unique analytical challenges.
• Coefficients of variation (CV) are important measures of relative variability.

Purpose of the Study:

• To develop and evaluate novel methods for constructing confidence intervals (CIs) for the difference between coefficients of variation (CV).
• To address the complexities of censored and zero-inflated gamma distributions.
• To provide robust statistical tools for analyzing environmental and other scientific data.

Main Methods:

• Fiducial inference based method adapted for censored zero-inflated gamma distributions.
• Box-Cox transformation method applied to both data and detection limits.
• Method of Variance Estimate Recovery (MOVER) to combine gamma and binomial distribution CI estimates.
• Monte Carlo simulations to assess method performance.

Main Results:

• All proposed confidence interval construction methods exhibited satisfactory performance.
• Evaluated metrics included coverage probability, average length, and tail error rates.
• The methods were validated using real-world precipitation data.

Conclusions:

• The developed methods offer reliable confidence intervals for the difference in CVs.
• These techniques are suitable for censored zero-inflated gamma distributions.
• The study provides practical tools for analyzing environmental and other scientific datasets.