Maximum Likelihood Estimation for Binomially Distributed Signals in Discrete Noise
Francisco J. Samaniego · Journal of the American Statistical Association · 1980
Let X be the sum of independent variables Y and Z, where Y is binomially distributed and Z is a nonnegative integer-valued variable whose distribution does not depend on the binomial parameter p. Convoluted binomial distributions describing variables like X are characterized by regularity conditions and equations of the form ∂/∂p P(X = x)=c[P(X = x − 1) − P(X = x)]. The characterization, together with a monotonicity property for probability ratios, is shown to facilitate maximum likelihood estimation of p. Results are applicable to models for binomial signals in noise in which the noise distribution is known or can be estimated from an auxiliary experiment.