Simultaneous inference for several quantiles of a normal population with applications.

Area of Science:

• Statistics
• Statistical Inference
• Quantitative Analysis

Background:

• Standard statistical inference often focuses on population means and variances.
• Real-world problems frequently necessitate understanding population quantiles, which incorporate both mean and variance.
• Simultaneous inference for multiple quantiles is an underexplored area.

Purpose of the Study:

• To construct exact simultaneous confidence intervals for several quantiles of a normally distributed population.
• To address the need for inference on multiple quantiles, motivated by practical applications.

Main Methods:

• Development of exact 1-α level simultaneous confidence intervals.
• Utilizing a simple random sample from the normally distributed population.
• Efficient computation of critical constants via numerical quadrature and search algorithms.

Main Results:

• A method for constructing exact simultaneous confidence intervals for multiple population quantiles is presented.
• The critical constants can be computed efficiently using a one-dimensional integral and standard search algorithms.
• The proposed methods are demonstrated with a practical example.

Conclusions:

• The study provides a statistically sound method for simultaneous quantile inference in normal distributions.
• The computational approach is efficient, making the methods practical for applications.
• Further research avenues in simultaneous inference are identified.