Abstract:
In practice, the proportion format data analyzing under the binomial assumption;
homogeneous success probability at each trial or count data analyzing under the Poisson
assumption; equi-dispersion constraint, the observed variance simply exceeds from the
expected variance. This context is explained by the over-dispersion and mostly it is
common in biomedical and criminology studies. In the potential solution part, two-stage
models that lead to compound mixed probability models for the responses allowing over dispersion, proposed to overcome this phenomenon. Our principle goal in this research is to
examine the work efficiency of the mixture of the Poisson and gamma: negative binomial
(NB) and the mixture of beta and NB: beta negative binomial (BNB) into the insurance
claim dataset that vary in the value of the sample index dispersion (𝜙). The Poisson, NB,
and BNB models fit by the maximum likelihood estimation (MLE), tested, and compared
based on the p-value of the 𝜒
2 goodness of fit test on fifteen different sets of insurance claim
frequency data that obtained from R packages covering the 𝜙 ranges from 1.053 to 3.154.
This study finds that NB and BNB fit better than Poisson handling over-dispersion in the
insurance claim datasets. It is observed that work efficiency of NB and BNB do not
consistent with 𝜙 values and comparatively for large value of 𝜙, the BNB is a better fit
than NB.
