Wikipedia
In the mathematical theory of probability, the combinants c of a random variableX are defined via the combinant-generating function G(t), which is defined from the moment generating function M(z) as
G(t) = M(log(1 + t))
which can be expressed directly in terms of a random variable X as
G(t) : = E[(1 + t)], t ∈ 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:
$$c_n = \frac{1}{n!} \frac{\partial ^n}{\partial t^n} \log(G (t)) \bigg|_{t=-1}$$
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.
Usage examples of "combinant".
The combinant, of course, and the reader on which his textbooks were stored, and his utility case, which was full of all manner of miniature devices for wayfarers that he had rarely bothered to inspect but which might very well come in handy now, wherever he might be going.
By the yellow light of the next bomb-burst Joseph located his combinant where he had set it down at the side of his bed, thumbed its command button, and waited for the blue globe betokening contact to take form in the air before him.
Normally it took no more than seconds for the combinant to make contact anywhere in the world.
But she would not go away, and his combinant did not seem to be working.
While Joseph waited for his clothes to dry he tried yet again to make combinant contact with his father, and once more failed.
I might just as well throw the combinant away, he thought, although he could not bring himself to do it.
He ate one of his remaining tubers, made another fruitless attempt to use his combinant, offered up the appropriate prayers for bedtime, and settled down for sleep.
The interruption in combinant communication alone would be indication enough that something was wrong.
He was experimenting with the still useless combinant once again, his first attempt with it in days, when there came a sound of reed-flute music from the corridor, the breathy, toneless music that had some special significance for the Indigenes, and then an Indigene of obvious grandeur and rank entered the room, a personage who very likely was the chieftain of the village, or perhaps the high priest, if they had such things as high priests.
Once he was established again in the room that had been his before, Joseph tried once more to make contact via combinant with Keilloran.
But at least the combinant was producing something, now, whereas it had done nothing whatever since the night of the burning of Getfen House.
If the combinant was working properly, that statement alone would suffice to connect him instantly.
He stared urgently into the pink glow, wishing that he were seeing the familiar blue of a functioning combinant instead.
The thought came to him then that what he had just said could have been very rash, that perhaps the combinant system of Manza was in rebel hands, in which case they might have intercepted his call and possibly could trace it to this very village.
He thought he would try the combinant one more time before setting out.