"Parametric" invariance requires the characteristics of each distribution to be identical over time and across different offense types. "Mathematical-form" invariance requires that a single class of mathematical functions, differing only in the parameter values, closely approximates each age-crime curve. To test for both types of invariance, this study fit two common probability density functions -- gamma and lognormal -- to the age distribution of index offenses in the United States from 1952 to 1987. Consistent with prior research, the results do not support parametric invariance. There is considerable support, however, for mathematical-form invariance. This support holds whether the gamma or lognormal results are considered. The model fits for both density functions are uniformly high, especially for property offenses and rape. 3 tables and 30 references
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