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Bivariate Distributions Constructed by the Conditional Approach

In: Continuous Bivariate Distributions

Author

Listed:
  • N. Balakrishna

    (McMaster University, Department of Mathematics & Statistics)

  • Chin Diew Lai

    (Institute of Sciences and Technology, Massey University)

Abstract

In Section 5.6, we outlined the construction of a bivariate p.d.f. as the product of a marginal p.d.f. and a conditional p.d.f., h(x,y)=f(x)g(y|x). This construction is easily understood, and has been a popular choice in the literature, especially when Y can be thought of as being caused by, or predicted from, X. Arnold et al. (1999, p. 1) contend that it is often easier to visualize conditional densities or features of conditional densities than marginal or joint densities. They cite, for example, that it is not unreasonable to visualize that, in the human population, the distribution of heights for a given weight will be unimodal, with the mode of the conditional distribution varying monotonically with weight. Similarly, we may visualize a unimodal distribution of weights for a given height, this time with the mode varying monotonically with the height. Thus, construction of a bivariate distribution using two conditional distributions may be practically useful.

Suggested Citation

  • N. Balakrishna & Chin Diew Lai, 2009. "Bivariate Distributions Constructed by the Conditional Approach," Springer Books, in: Continuous Bivariate Distributions, chapter 0, pages 229-278, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-09614-8_7
    DOI: 10.1007/b101765_7
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