Category: Characterization of probability distributions

In probability and statistics, memorylessness is a property of certain probability distributions. It usually refers to the cases when the distribution of a "waiting time" until a certain event does no
Raikov's theorem
Raikov’s theorem, named for Russian mathematician Dmitrii Abramovich Raikov, is a result in probability theory. It is well known that if each of two independent random variables ξ1 and ξ2 has a Poisso
Lukacs's proportion-sum independence theorem
In statistics, Lukacs's proportion-sum independence theorem is a result that is used when studying proportions, in particular the Dirichlet distribution. It is named after Eugene Lukacs.
Cramér's decomposition theorem
Cramér’s decomposition theorem for a normal distribution is a result of probability theory. It is well known that, given independent normally distributed random variables ξ1, ξ2, their sum is normally
Characterization of probability distributions
In mathematics in general, a characterization theorem says that a particular object – a function, a space, etc. – is the only one that possesses properties specified in the theorem. A characterization
Cochran's theorem
In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance.