Contents
Which distribution does not have moment generating function?
So one way to show that t distributions do not have moment generating functions is to show that not all moments exist. But it is well known that the t-distribution with ν degrees of freedom only have moments up to order ν−1, so the mgf do not exist.
What does a moment-generating function do?
MGF encodes all the moments of a random variable into a single function from which they can be extracted again later. A probability distribution is uniquely determined by its MGF. If two random variables have the same MGF, then they must have the same distribution.
What does MFG stand for on medicine?
manufacturing date
‘Mfg’ stands for the manufacturing date. Previously, USP guidelines required supplement manufacturers to state an expiration date, ‘Best before’, ‘Use by’ or ‘Sell by’, date. The guidelines were revised by the FDA to include an ‘mfg’ date as well.
When does the moment generating function ( MGF ) do not exist?
. The moment generating function (mgf) of in some neighborhood of 0. That is, there is an exists. If the expectation does not exist in a neighborhood of 0, we say that the moment generating function does not exist. . More generally, when
What are the properties of a moment generating function?
Besides helping to find moments, the moment generating function has an important property often called the uniqueness property. The uniqueness property means that, if the mgf exists for a random variable, then there one and only one distribution associated with that mgf. Therefore, the mgf uniquely determines the distribution of a random variable.
Is the moment generating function of a distribution always the same?
The moment-generating function of a real-valued distribution does not always exist, unlike the characteristic function. There are relations between the behavior of the moment-generating function of a distribution and properties of the distribution, such as the existence of moments.
Is the moment generating function of a lognormal distribution not existent?
In Casella and Berger (2002) I found a proof for the moment-generating function (mfg) of a lognormal distribution not being existent (see exercise 2.36 on page 81 and the answer provided here on page 2-12). Starting point is the following lognormal pdf (with μ = 0 and σ 2 = 1 ): lim x → ∞ e t x − ( l n ( x)) 2 = ∞.