15) have established explicit expressions and some recurrence relations for moment generating function
of generalized order statistics from Gompertz distribution.
In this paper, we use the method of moment generating function
(mgf) to derive the probability distribution of the sum of k dice, for [k.
where [psi](t) is the moment generating function
of density p([lambda]) and
X is said to be smaller than Y in moment generating function
ordering, denoted by X [[less than or equal to].
In particular, a closed-form expression for the moment generating function
(MGF) of the Weibull random variable (RV) was obtained in  when the Weibull fading parameter is restricted to integer values.
Hwang's results, the so-called quasi-power theorem, give a central limit theorem and convergence rate for a sequence of random variables with moment generating function
obeying a quasi-power form (that is, the moment generating function
is asymptotically exponential).
Moreover the logarithmic moment generating function
The associated Moment Generating Function
of the Poisson distribution is:
It is of interest to note that the confluent hypergeometric function, M, yields the prior moment generating function
of p from density (1).
tz]) = the moment generating function
of Z with auxiliary parameter t.
The moment generating function
(MGF)-based approach for performance analysis, introduced by the authors in the first edition and referred to in literally hundreds of publications, still represents the backbone of the books presentation.
It is also shown from an analysis of the moving poles of the Mellin transform of the poissonized moment generating function
that the imbalance factor (under appropriate centering and scaling) follows a Gaussian limit law.