Neyman-Pearson confidence intervals for extreme low-level, paired counting

Area of Science:

• Statistics
• Probability Theory
• Applied Mathematics

Background:

• The Neyman-Pearson framework is fundamental for hypothesis testing.
• Poisson distributions are common for count data in scientific research.
• Accurate confidence intervals are essential for reliable statistical inference.

Purpose of the Study:

• To derive and present 95% confidence intervals for the difference between two Poisson-distributed random variables.
• To explore the application of modified Bessel functions in constructing these intervals.
• To discuss the validity and interpretation of the obtained confidence interval values.

Main Methods:

• The study utilizes Neyman-Pearson principles.
• It employs modified Bessel functions of integral order and elementary functions.
• The probability distribution of the difference between two Poisson variables is mathematically derived.

Main Results:

• 95% confidence intervals of the form [0, ##.##] are presented.
• The derived intervals are based on the properties of modified Bessel functions.
• The validity of the calculated confidence interval values is assessed.

Conclusions:

• The application of modified Bessel functions provides a valid method for calculating confidence intervals for the difference of Poisson variables.
• The presented confidence intervals offer a practical tool for statistical analysis in fields utilizing Poisson distributions.
• Further discussion on the validity ensures the reliable application of these statistical methods.