Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-02T22:00:05.670Z Has data issue: false hasContentIssue false
  • English
  • Français

Properties of Conditionally Independent Generalized Gamma Distributions

Published online by Cambridge University Press:  27 July 2009

Mel-Ling Ting Lee  and
Alan J. Gross*
Mel-Ling Ting Lee
Affiliation:
Academia Sinica Taipei 11529, Taiwan, Republic of China and Boston University Boston, Massachusetts 02215
Alan J. Gross*
Affiliation:
Medical University of South Carolina Charleston, South Carolina 29403 and The Food and Drug Administration Rockville, Maryland 20857
Get access Rights & Permissions [Opens in a new window]

Abstract

Models of life time observations that have conditionally independent generalized gamma distributions are investigated. Positive dependency among the unconditional joint distribution is discussed. General formula for moment inequalities are given. Conditional hazard rate, mean residual life functions, and bounds for system reliabilities are also discussed. An application was given.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 2 , April 1989 , pp. 289 - 297
Copyright
Copyright © Cambridge University Press 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: TO BEGIN WITH.Google Scholar
Block, H.W. & Ting, M.-L. (1981). Some concepts of multivariate dependence. Communications in Statistics A 10(8): 749–772.Google Scholar
Cantor, A.B. & Knapp, R.G. (1985). A test of the equality of survival distributions, based on paired observations from conditionally independent exponential distributions. IEEE Transactions on Reliability R-34 (4): 342–346.CrossRefGoogle Scholar
Gross, A.J. & Lam, C.F. (1981). Paired observations from a survival distribution. Biometrics 37: 505–511.CrossRefGoogle Scholar
Karlin, S. (1968). Total positivity, Vol. 1. Stanford, California: Stanford University Press.Google Scholar
Karlin, S. & Rinoit, Y. (1980). Classes of orderings of measures and related correlation inequalities, I. Journal of Multivariate Analysis 10: 467–498.CrossRefGoogle Scholar
Knapp, R.G., Gross, A.J., & Cantor, A.B. (1986). A likelihood ratio test of the equality of paired survival data with censoring. Biometrics Journal 28(6): 665–672.CrossRefGoogle Scholar
Lee, M.-L.T. (1985). Dependence by total positivity. Annals of Probability 13 (2): 572–582.CrossRefGoogle Scholar
Lindley, D.V. & Singpurwalla, N.D. (1986). Multivariate distributions for the life lengths of components of a system sharing a common environment. Journal of Applied Probability 23: 418–431.CrossRefGoogle Scholar
Frentice, R.L. (1974). A log-gamma model and its maximum likelihood estimation. Biometrika 61 (3): 539–544.CrossRefGoogle Scholar
Shaked, M. (1977). A concept of positive dependence for exchangeable random variables. Annals of Statistics 5(3): 505–515.Google Scholar
Shaked, M. (1977). A family of concepts of dependence for bivariate distributions. Journal of the American Statistical Association 72: 642–650.CrossRefGoogle Scholar
Stacy, E.W. (1962). A generalization of the gamma distribution. Annals of Mathematical Statislics 33: 1187–1192.CrossRefGoogle Scholar