POISSON BAGUI-LIU-ZHANG DISTRIBUTION: A FLEXIBLE MIXED-POISSON MODEL FOR HEAVY-TAILED COUNT DATA
Abstract
Some over-dispersed count poses varying characteristics such as uni-modal or multi-modal,
right or left skewed, platokurtic or leptokurtic and therefore requires more flexible discrete
distributions than the existing ones in order to minimize estimation error. A new discrete
distribution named Poisson Bagui-Liu-Zhang distribution for modelling over-dispersed count
data has been proposed and its properties such as - hazard function, probability generating
function, characteristic function, rth factorial moment, raw and central moments, the
dispersion index, the coefficient of variation, the coefficient of skewness and the coefficient
kurtosis - derived. Conventional estimation methods were used to obtain the estimators for
the parameter of the distribution and their performances compared using simulated data. The
results from the simulation study showed that the maximum likelihood estimator and the
method of proportion estimator of the distribution, have positive bias and showed consistency
property while the method of moment estimator and weighted least squares estimator were
not consistent and were negatively biased. Generally, the maximum likelihood estimator of
the new distribution performed better than the other estimators obtained. Again the new
distribution was fitted to two real life data sets and its performance compared to that of the
Poisson-Lindley distribution, the Poisson-Akash distribution, the Poisson-Bilal distribution,
the geometric distribution and the negative binomial distribution. The results from the data
sets, with features; dispersion indices (419.13, 3.527), positive skeweness (3.50, 3.44) and
leptokurtic (15.38, 15.69), showed that the new distribution, having produced the minimum
values of Akaike information criterion (565.6158, 401.7164), Bayesian information criterion
(567.4000,404.4259), negative loglikelihood (281.8079,199.8582) and the highest values
Klomogrov-Smirnov/p-value (0.1651/0.3200,0.0942/0.1351) respectively for the two data
sets, performed better than the other distributions.
