Abstract: For
the negative binomial model (probability generating function a logarithmic derivative is the Psi
function difference this and its derivatives lead to a
test statistic to decide on the validity of a specified model. The test
statistic uses a data base so there exists a comparison available between theory
and application. Note that the test function is not dominated by outliers. Applications
to (i) Fisher’s tick data, (ii) accidents data, (iii) Weldon’s dice data are
included.
Keywords and phrases: accident data,
logarithmic derivatives, maximum likelihood estimator, moment estimator,
Weldon’s dice data.
