Editing Gamma distribution (section)

===Summation===
If {{math|''X''<sub>''i''</sub>}} has a {{math|Gamma(''α''<sub>''i''</sub>, ''θ'')}} distribution for {{math|1=''i'' = 1, 2, ..., ''N''}} (i.e., all distributions have the same scale parameter {{mvar|θ}}), then

<math display=block>  \sum_{i=1}^N X_i \sim\mathrm{Gamma}  \left( \sum_{i=1}^N \alpha_i, \theta \right)</math>

provided all {{math|''X''<sub>''i''</sub>}} are [[statistical independence|independent]].

For the cases where the {{math|''X''<sub>''i''</sub>}} are [[statistical independence|independent]] but have different scale parameters, see Mathai <ref>{{Cite journal|last=Mathai|first=A. M.|title=Storage capacity of a dam with gamma type inputs|journal=Annals of the Institute of Statistical Mathematics|language=en|volume=34|issue=3|pages=591–597|doi=10.1007/BF02481056|issn=0020-3157|year=1982|s2cid=122537756}}</ref> or Moschopoulos.<ref>{{cite journal |first=P. G. |last=Moschopoulos |year=1985 |title=The distribution of the sum of independent gamma random variables |journal=Annals of the Institute of Statistical Mathematics |volume=37 |issue=3 |pages=541–544 |doi=10.1007/BF02481123 |s2cid=120066454 }}</ref>

The gamma distribution exhibits [[Infinite divisibility (probability)|infinite divisibility]].