• Shelby J. Haberman
Part of the Springer Series in Statistics book series (SSS)


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.


Real Function Positive Real Number Central Moment Finite Population Linear Lattice 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Shelby J. Haberman
    • 1
  1. 1.Department of StatisticsNorthwestern UniversityEvanstonUSA

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