eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2022-03-15 10 1 14 21 10.12691/ajams-10-1-3 AJAMS20221013 article Arnold Kiura Njuki kiurarnold@gmail.com 1 Thomas Mageto 1 Anthony Ngunyi 2 Department of Statistics and Acturial Sciences, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya Department of Statistics and Acturial sciences, Dedan Kimathi University of Technology, Nyeri, Kenya Biometric authentication system has become a mainstream solution across industries and devices. From securing highly confidential data to unlocking smartphones, biometrics have eliminated the hassle of remembering multiple complex passwords and PINs. It means that nobody can gain access to a device or system without your presence. This paper discusses a method which could be used in the testing process of biometric systems on the side of users and customers. Large ¨Cscale biometric systems traditionally undergo a series of tests beyond technology and scenario testing. These large-scale system tests are typically at the system level, not just the biometric subsystem level, and occur multiple times in the life of a system in such forms as factory acceptance tests before shipment, site or system acceptance tests before initiating operations, and in- use tests to ensure that performance remains at acceptable levels and/or to reset thresholds or other technical parameters. The conventional statistical methods use the binomial distribution to estimate the expected number of failure, but in the field of the biometrics the probability parameter can¡¯t be constant which means that it is necessary to describe a process. The results have shown that the probability is characterized with two parameters of the beta distribution, and these are predictable from a smaller sample of the investigated population with the maximum likelihood method. http://pubs.sciepub.com/ajams/10/1/3/ajams-10-1-3.pdf format microsoft word template style insert template