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The use of correlated binomial distribution in estimating error rates for firearm evidence identification



Nien F. Zhang


In forensic science on firearm evidence identification, estimating error rates is a fundamental challeng. Recently, a quantitative approach known as the congruent matching cells (CMC) method was developed to improve the accuracy of ballistic identifications and provided a base for estimating error rates. To estimate error rates, the key is to find an appropriate probability distribution for the relative frequency distribution of the observed CMC measurements. Until now, some the probability models have been proposed. However, the assumption of independence among the cell pair comparisons from CMC method may not be valid. This article proposes statistical models based on dependent Bernoulli trials and the corresponding methodology for parameter estimation. In addition, to demonstrate the improvement, the methododlogy applies to an actual data set of fired catridge cases.
Journal of Research (NIST JRES) -


Beta distribution, congruent matching cells, dependent Bernoulli trials, forensic science, maximum likelihood estimator, nonlinear regression model


Zhang, N. (2019), The use of correlated binomial distribution in estimating error rates for firearm evidence identification, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 27, 2024)


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Created October 1, 2019, Updated June 24, 2021