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Equations to Describe Population Based Parametric Mixtures of Logistic Regressions

Joint density of birth weight and occurrence of death for the 2-subpopulation case

Birth-weight density:

 is the mixing proportion
 is the Gaussian density with mean  and variance  truncated at 0.

Probability of death conditioned on birth:

An infant of birth weight x in the ith sub-population has probability of dying given in quadratic logistic form:

 is the probability that this child is from sub-population 1 given it has birth weight x.