Min entropy

In the mathematical theory of probability, the combinants c_n of a random variable X are defined via the combinant-generating function G(t), which is defined from the moment generating function M(z) as

$G_X(t)=M_X(\log (1+t))$

which can be expressed directly in terms of a random variable X as

$G_X(t):=E[(1+t{)}^X],t\in \mathbb{ℝ},$

wherever this expectation exists.

The nth combinant can be obtained as the nth derivatives of the logarithm of combinant generating function evaluated at –1 divided by n factorial:

$c_n=\frac{1}{n!}\frac{{\partial }^n}{\partial t^n}\log (G(t)){|}_{t=-1}$

Important features in common with the cumulants are:

• the combinants share the additivity property of the cumulants;
• for infinite divisibility (probability) distributions, both sets of moments are strictly positive.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Google Books

Template:Theory of probability distributions