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Bivariate distributions with equi-dispersed normal conditionals and related models

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Listed:
  • Barry C. Arnold

    (University of California)

  • B. G. Manjunath

    (University of Hyderabad)

Abstract

A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes a one parameter exponential family. In the present article our main focus is on univariate and bivariate models with equi-dispersed normal component distributions. We discuss distributional features of such models, explore inferential aspects and include an example of application of equi-dispersed models. Some related models are discused in Appendices.

Suggested Citation

  • Barry C. Arnold & B. G. Manjunath, 2024. "Bivariate distributions with equi-dispersed normal conditionals and related models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(4), pages 427-448, May.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:4:d:10.1007_s00184-023-00921-5
    DOI: 10.1007/s00184-023-00921-5
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    References listed on IDEAS

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    1. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose María, 1994. "A conditional characterization of the multivariate normal distribution," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 313-315, March.
    2. E. Castillo & J. Galambos, 1989. "Conditional distributions and the bivariate normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 209-214, December.
    3. Arnold, Barry C. & Castillo, Enrique & Sarabia, José María & González-Vega, Laureano, 2000. "Multiple modes in densities with normal conditionals," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 355-363, October.
    Full references (including those not matched with items on IDEAS)

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