Bivariate inverse gaussian distribution

  • Essam K. Al-Hussaini
  • Nagi S. ABD-El-Hakim
Article

Summary

A bivariate inverse Gaussian (IG) density function is constructed. Relations of the bivariate IG distribution to the normal and χ2 distributions are established. The corresponding bivariate random walk (RW) density function is obtained. The properties and behaviour of bivariate IG distribution are studied for large parametric values. Moment estimates of the five parameters are given and applications are pointed out. A generalization to the multivariate IG distribution is proposed.

Keywords

Density Function Random Walk Bivariate Distribution Inverse Gaussian Distribution Positive Drift 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Chhikara, R. S. and Folks, J. L. (1974). Estimation of the inverse Gaussian distribution function,J. Amer. Statist. Ass.,69, 250–254.MATHCrossRefGoogle Scholar
  2. [2]
    Parzen, E. (1962).Modern Probability Theory and Its Applications, third printing, Wiley, 292.Google Scholar
  3. [3]
    Shuster, J. (1968). On the inverse Gaussian distribution function,J. Amer. Statist. Ass.,63, 1514–1516.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Tweedie, M. C. K. (1957). Statistical properties of inverse Gaussian distributions I,Ann. Math. Statist.,28, 362–377.MATHMathSciNetGoogle Scholar
  5. [5]
    Wasan, M. T. (1969).First Passage Time Distribution of Brownian Motion with Positive Drift (Inverse Gaussian Distribution), Queen's papers in pure and applied mathematics, Queen's University, Canada, 208–209.Google Scholar

Copyright information

© Kluwer Academic Publishers 1981

Authors and Affiliations

  • Essam K. Al-Hussaini
    • 1
  • Nagi S. ABD-El-Hakim
    • 1
  1. 1.University of AssiutAssiutEgupt

Personalised recommendations