Improved confidence intervals when the sample is counted an integer times longer than the blank

Area of Science:

• Statistics
• Nuclear Counting
• Data Analysis

Background:

• Accurate confidence intervals are crucial for paired counting data analysis.
• Existing methods for confidence intervals in paired counting have limitations.
• The ratio of sample count time to blank count time (IRR) is often an integer in practical applications.

Purpose of the Study:

• To extend existing computer solutions for confidence intervals in paired counting.
• To address scenarios where the integer ratio of sample count time to blank count time (IRR) is applicable.
• To develop a method for calculating the probability density function (PDF) of net counts.

Main Methods:

• The study extends past computational techniques for confidence intervals.
• It employs a method similar to Pearson and Hartley's tabulation for Poisson and Binomial distributions.
• Assumes blank counts and sample contributions to gross counts are Poisson distributed with a known expected blank count.

Main Results:

• A method is presented for calculating confidence intervals in paired counting with an integer IRR.
• The probability density function (PDF) for the net count (OC) is derived.
• The approach clarifies the nomenclature of confidence intervals, favoring 'Neyman confidence intervals' or 'confidence intervals' over 'Neyman-Pearson confidence intervals'.

Conclusions:

• The developed technique provides a robust method for confidence interval estimation in paired counting with integer IRR.
• This work refines the understanding and application of statistical methods in counting experiments.
• The straightforward derivation of the net count's PDF facilitates further statistical analysis.