Moments are commonly used to describe the distributions of real random variables and random vectors, and they are often used with real measurable functions and measurable vectors. Pearson (1894) is a good early example of their use in statistics. In Section 8.1, moments are defined for real measurable functions, and their basic properties are reviewed. In Section 8.2, moment-generating functions, cumulant-generating functions, cumulants, and characteristic functions are defined for real measurable functions. In Section 8.3, moments, moment-generating functions, and characteristic functions are considered for vector-valued measurable functions.
KeywordsReal Function Positive Real Number Central Moment Finite Population Linear Lattice
Unable to display preview. Download preview PDF.