Fast algorithms of computing admissible intervals for discrete distributions with single parameter.

Area of Science:

• Statistical inference
• Computational statistics
• Probability theory

Background:

• Accurate confidence intervals are crucial for parameter estimation in various statistical distributions.
• Existing methods may be computationally intensive or lack exactness for certain parameters.
• Applications span disease analysis, quality control, and risk assessment.

Purpose of the Study:

• To develop efficient algorithms for computing optimal exact confidence intervals.
• To address parameters including binomial success probability (p), hypergeometric counts (M, N), and Poisson mean (λ).
• To handle scenarios with large sample sizes (n) or observations (X).

Main Methods:

• Proposed efficient algorithms for constructing exact confidence intervals.
• Focus on parameters from binomial, hypergeometric, and Poisson distributions.
• Algorithm validation through practical examples and performance analysis.

Main Results:

• The developed algorithms compute admissible exact intervals.
• Demonstrated shorter interval lengths compared to existing methods.
• Achieved significant improvements in computational speed and efficiency.

Conclusions:

• The proposed algorithms offer accurate and time-efficient solutions for computing exact confidence intervals.
• These methods enhance statistical analysis in diverse practical applications.
• The findings contribute to more reliable and faster statistical estimations.