We present new developments regarding positive empirical models of election frauds. We develop a general Bayesian framework using finite mixture models of product distributions to identify the probability and distribution of frauds in elections. The framework is based on transformations of random variables that capture incremental and extreme frauds inspired by the work of Klimek et al (2012). A formulation that closely matches their specifications is a special case. The framework can be used with a larger class of probability distributions (i.e. parametric and distributional assumptions) than the original model that includes a mixture of restricted normal distributions. The general formulation explicitly models effects of covariates associated with voters’ behavior and with the occurrence of frauds. We present logistic-binomial and restricted Normal variants of the general model. We present an extension intended to handle absentee/mail precincts, where we do not observe how many electors acted in each type of election unit. We use simulated data to show that the logistic-binomial model can be estimated well using MCMC methods and that the estimates have good frequentist coverage properties when the model is correctly specified. Estimates are not as good when relevant covariates are ignored.