Note that the sampling process for estimating the probability matrix P G is a binomial process, which, by the central limit theorem, is closely approximated by a normal distribution.
Binomial distribution, in statistics, a common distribution function for discrete processes in which a fixed probability prevails for each independently generated value.
Such a process would be modeled by a binomial distribution, in which the second observation lies between the values of the first and third observation only one-third of the time.
Rice TARs were scored using a method based on the binomial theorem in which at least five consecutive probes whose intensities lie in the 80th percentile were identified [24].
We conclude that the zero-inflated negative binomial (ZINB) model, in which the parent distribution is specified to follow a negative binomial distribution as in equation (6), is the best fit for our data.
The Poisson distribution is frequently adopted because the Bernoulli process at the individual level (surgery vs non surgery) becomes a Binomial process at the area level, which can be approximated by the Poisson distribution when rare events are modelled [ 10].
However, there is no research work concerning the change-point estimation of multivariate binomial processes, whereas in many situations, monitoring processes containing several quality characteristics of attribute type, each following a binomial distribution, is a need.
We assume this to be the ratio of successful outcomes and failure outcomes in a binomial process.
In this section, we assume that the real change type presented in a multivariate binomial process is a step change and derive the MLE of a change point in the process fraction non-conforming.
In the 'Multivariate binomial process modeling and MLE derivation' section, the model of the process behavior is described and the MLEs of a step-change and a linear-trend disturbance are derived.
