A family of random variables closed under reciprocation

Journal of the American Statistical Association

Volumn 69, Issue 346, 1974, Pages 533-539

  Saunders, Sam C ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347051961     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1974.10482988     Document Type: Article

References (13)

1. Bastinaire, F., “A Study of the Scatter of Fatigue Test Results by Statistical and Physical Methods,” in W. Barrois and F.L. Ripley, eds., Fatigue of Aircraft Structures, New York: The Macmillan Company, 1963.
2. Besuner, P.M. and Whittaker, I.C., “A Reliability Analysis Approach to Fatigue Life Variability of Aircraft Structures,” Air Force Materials Laboratory Technical Report, AFML-TR-69-65, 1969.
3. Birnbaum, Z.W. and Saunders, S.C., “A New Family of Life Distributions,” Journal of Applied Probability, 6 (August 1969), 319–27.
4. —— and Saunders, S.C., “A Probabilistic Interpretation of Miner’s Rule,” SIAM Journal on Applied Mathematics, 16 (May 1968), 637–52.
5. —— and Saunders, S.C., “Estimation for a Family of Life Distributions with Applications to Fatigue,” Journal of Applied Probability, 6 (August 1969), 328–47.
6. Esary, J.D. and Marshall, A.W., “Coherent Life Functions,” SIAM Journal of Applied Mathematics, 18 (June 1970), 810–14.
7. Feller, William, An Introduction to Probability Theory and Its Applications, Vol. 2, New York: John Wiley and Sons, Inc., 1966, 439.
8. Marshall, A.W. and Proschan, F., “Classes of Distributions Applicable in Replacement with Renewal Theory Implications,” Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, 1, Theory of Statistics, Berkeley: University of California Press, 1972, 395–415.
9. McShane, E.J. and Botts, T.A., Real Analysis, Princeton, N.J.: D. Van Nostrand Co., Inc., 1959, 189.
10. Saunders, S.C., “A Probabilistic Interpretation of Miner’s Rule—II,” SIAM Journal of Applied Mathematics, 19 (July 1970), 251–65.
11. ——, “On the Probabilistic Determination of Scatter Factors Using Miner’s Rule in Fatigue Life Studies,” Proceedings of the American Society for Testing and Materials Symposium; Probabilistic Aspects of Fatigue, Philadelphia: American Society for Testing and Materials, Robert A. Heller, ed., 1972, 185–203.
12. Seshadri, V., “On Random Variables Which Have the Same Distribution as Their Reciprocals,” Canadian Mathematical Bulletin, 8, No. 6 (1965), 819–24.
13. Shuster, Jonathan, “On the Inverse Gaussian Distribution Function,” Journal of the American Statistical Association, 63 (December 1968), 1514–17.