Multidimensional Densities

  • Anirban DasGupta
Part of the Springer Texts in Statistics book series (STS)


Similar to the case of several discrete random variables, in applications we are frequently interested in studying several continuous random variables simultaneously. An example would be a physician’s measurement of a patient’s height, weight, blood pressure, electrolytes, and blood sugar. Analogous to the case of one continuous random variable, again we do not talk of pmfs of several continuous variables but of a pdf jointly for all the continuous random variables. The joint density function completely characterizes the joint distribution of the full set of continuous random variables. We refer to the entire set of random variables as a random vector. Both the calculation aspects and the application aspects of multidimensional density functions are generally sophisticated. As such, using and operating with multidimensional densities are among the most important skills one needs to have in probability and statistics. The general concepts and calculations are discussed in this chapter. Some special multidimensional densities, and in particular the multivariate normal density, are introduced separately in the next chapter.


Conditional Expectation Conditional Variance Conditional Density Joint Density Marginal Density 
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  1. David, H.A. (1980). Order Statistics, Wiley, New York.Google Scholar
  2. Tong, Y.L. (1990). The Multivariate Normal Distribution, Springer-Verlag, New York.Google Scholar

Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  1. 1.Dept. Statistics & MathematicsPurdue UniversityWest LafayetteUSA

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