A family of survival distributions that are mixtures of one group which fails according to
an exponential law with another group that does not fail has recently come into use in
correctional program evaluation. The concept is generalized to include mixtures based on
the Weibull distribution. Available graphical and numeric goodness-of-fit tests are
discussed and a new test for grouped, multiply censored data due to Turnbull and Weiss
(1978) is used to discriminate between the various special cases in this family of mixtures.
The goodness-of-fit test is also extended to allow k group tests of hypotheses on the
parameters.
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