# moment generating function

## moment generating function

[¦mō·mənt ¦jen·ə‚rād·iŋ ′fəŋk·shən]
(statistics)
For a frequency function ƒ (x), a function φ(t) that is defined as the integral from -∞ to ∞ of exp(tx) ƒ(x) dx, and whose derivatives evaluated at t = 0 give the moments of ƒ.
References in periodicals archive ?
for 0 [less than or equal to] s < t and x [member of] R, where [M.sub.Y](x) is the moment generating function of the Gamma distribution.
The moment generating function (m.g.f.) of a random variable X is denoted by [M.sub.X](t) and defined by
Based on the proposed model, the joint moment generating function of underlying log-asset price and counter's log-asset value is derived.
Several mathematical properties of the EE distribution, including expectation, variance, moment generating function (mgf), asymmetry and kurtosis coefficients, among others, were studied by Gomez et al.
Proof: The moment generating function of X and Y is given by:
The moment generating function of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has the asymptotic expansion
The proposed estimator is based on moment generating function and is compared with maximum likelihood estimator using the mean squared error as a performance criterion.
In this section, we initially provide an analytical expression for the moment generating function of the Muth distribution in terms of the exponential integral function.
Using approximations for the exponential moment generating function, BER expressions are derived in  for the product of K-function distributions.
The relation in (2.1) will be used to derive some recurrence relations for the moment generating function of lgos from extended type I generalized logistic distribution.
The Moment Generating Function (mgf) of a random variable X is defined as (Scheaffer and Young, 2009) the expected value or weighted average of the function [e.sup.tx]:
where [psi](t) is the moment generating function of density p([lambda]) and
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