Sum of Bernoulli mixtures: Beyond conditional independence

We consider the distribution of the sum of bernoulli mixtures under a general dependence structure. the level of dependence is measured in terms of a limiting conditional correlation between two of the bernoulli random variables. the conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. the large-sample distribution of the empirical frequency and its use in approximating the risk measures,value at risk and conditional tail expectation,are presented for a new class of models which we call double mixtures. several illustrative examples with a beta mixing distribution,are given. as well,some data from the area of credit risk are fit with the models,and comparisons are made between the new models and also the classical beta-binomial model. © 2014 taehan bae and ian iscoe.