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The break-by-one gamma distribution has a probability density function resembling the Schechter function, but with the small-argument behavior modified so it is normalizable in commonly arising cases where the Schechter function is not. Its connection to the gamma distribution makes it straightforward to sample from. These properties make it useful for cosmic demographics.

The Break-by-one Gamma Distribution: A Proper and Tractable Alternative to the Schechter Function for Modeling Cosmic Populations