Inference on Two-Parameter Maxwell Distribution: Two-Sample Case

Oregon Convention Center 

The two-parameter Maxwell distribution is commonly used in life-testing and reliability analysis due to its smoothly increasing failure rate. Our study focuses on constructing confidence intervals (CIs) for the difference between means and ratio of means of two independent Maxwell distributions. We propose CIs based on the fiducial approach, approximate fiducial approach (also known as modified normal-based approximation), and parametric bootstrap (PB) method. We compare these methods based on their coverage probability and precision. We extend these methods to find CIs for a difference between percentiles and a ratio of two independent Maxwell distributions. Specifically, we develop and evaluate CIs for the ratio of the 5th percentiles and the ratio of the medians for coverage probability and precision accuracy. We illustrate these methods using two examples with real-life data. Although the PB confidence intervals are more efficient than the fiducial CIs in some situations, the approximate fiducial CIs are very simple to compute and are comparable with the PB CIs in most cases.

coverage probability

equivariant estimator

fiducial method

location-scale family

MLEs

PB approach 

Section on Statistical Computing