Les lois Gamma restreintes, leurs variantes, leurs moments et quelques bribes de leurs distributions Time-constrained Gamma variables, their variants, moments and distribution
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Constrained Gamma distributions
, Cumulative triggering function
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The Gamma (or Erlang) variable with integer parameter $k$ can be seen as a global duration obtained through summing $k$ successive individual delays, each one following a standard exponential distribution. What does happen to the Gamma variable if an upper bound is placed either on the individual delays or on their combined duration while the summing of delays continues until the chosen criterion is met? We devised and studied seven likely variants of the constrained Gamma variable, for some of which statistical moments and probability distribution are furnished.