ABSTRACT
This appendix is intended to provide a quick reference for selected properties
of distributions commonly used for data analysis, evaluation, and assimilation.
For further reference, note that the moment generating function (MGF),
denoted in this appendix as Mx (t), is defined as the expectation of e tx, namely
Mx (t) = E (e tx) =
etx p (x) dx , where x is a random variable and t is a
real number. The multivariate MGF is defined analogously as
Mx (t) = E
( exp
( n∑ i=1
xiti
)) =
exp
( n∑ i=1
xiti
) p (x) dx, (6.1)
where the vector (t1, t2, . . . , tn) has components ti defined symmetrically
around the origin (0, 0, . . . , 0), namely −toi < ti < toi, with toi > 0, (i = 1, . . . , n).
