Confidence intervals for low-level, paired counting

Area of Science:

• Statistics
• Probability Theory
• Applied Mathematics

Background:

• Neyman-Pearson principles are fundamental in hypothesis testing.
• Poisson distributions are commonly used to model count data.
• Confidence intervals are essential for quantifying uncertainty in statistical estimates.

Purpose of the Study:

• To present a method for calculating 95% confidence intervals for the difference between two Poisson distributed random variables.
• To explore the application of modified Bessel functions in this statistical context.

Main Methods:

• The study utilizes the relationship between the probability of the difference of two Poisson variables and modified Bessel functions of integral order.
• Neyman-Pearson principles are referenced to frame the confidence interval construction.
• The calculation involves elementary functions alongside Bessel functions.

Main Results:

• The research presents 95% confidence intervals of the form [0, ##.##].
• The validity and applicability of the derived confidence interval values are discussed.

Conclusions:

• The proposed method provides a statistically sound approach for estimating the difference between two Poisson distributions.
• The use of modified Bessel functions offers a novel way to compute these confidence intervals.