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4.8 Suggestions for Further Reading 131

for a detailed discussion of the relationship between characteristic functions and moment-generating
functions.
Stuart and Ord (1994, Chapter 3) gives a comprehensive discussion of cumulants; in particular,
this reference contains extensive tables relating cumulants to moments and central moments. Another
excellent reference on cumulants is McCullagh (1987) which emphasizes the case of vector-valued
random variables and the properties of cumulants under transformations of the random variable.
Cram´er (1946, Chapter 27) gives many results on the moments, central moments, and cumulants of
the sample mean; similar results are also given for the sample variance, a topic that is not considered
here. Conditional cumulants are discussed in McCullagh (1987, Section 2.9); the approach used in
Section 4.6 to relate unconditional and conditional cumulants is based on Brillinger (1969).