Generalized negative binomial distribution: a promising statistical distribution for Oncomelania hupensis in the lake- and marsh-land regions of China.

A new generalization of the negative binomial distribution (GNBD) is introduced and fitted to counts of Oncomelania hupensis, the intermediate host of Schistosoma japonicum, made, in areas of Chinese lakeland and marshland, early in the winter of 2005 and late in the spring of 2006. The GNBD was found to fit the snail data better than the standard negative binomial distribution (NBD) that has previously been widely used to model the distribution of O. hupensis. With two more parameters than the NBD, the GNBD can integrate many discrete distributions and is more flexible than the NBD in modelling O. hupensis. It also provides a better theoretical distribution for the quantitative study of O. hupensis, especially in building an accurate prediction model of snail density. The justification for adopting the GNBD is discussed. The GNBD allows researchers to broaden the field in the quantitative study not only of O. hupensis and schistosomiasis japonica but also of other environment-related helminthiases and family-clustered diseases that have, traditionally, been modelled using the NBD.