On characterizations based on record values and order statistics

Journal of Statistical Planning and Inference

Volumn 63, Issue 2, 1997, Pages 271-284

  Nagaraja, H N ^a   Nevzorov, V B ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Characterization; Moment sequences; Order statistics; Record values; Regression; Truncated distribution

Indexed keywords

EID: 0031572735     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(97)84450-3     Document Type: Article

References (28)

1. Barlow, R.E., Proschan, F., 1981. Statistical Theory of Reliability and Life Testing, To Begin With, Silver Spring.
2. Deheuvels, P., 1984. The characterization of distributions by order statistics and record values - a unified approach. J. Appl. Probab. 21 326-334. (Correction 22, 1985, 997).
3. Feller, W., 1965. An Introduction to Probability Theory and Its Applications. Wiley, New York.
4. Ferguson, T.S., 1967. On characterizing distributions by properties of order statistics. Sankhyā A 29, 265-278.
5. Galambos, J., Kotz, S., 1978. Characterizations of Probability Distributions. Lecture Notes in Mathematics No. 675, Springer, Berlin.
6. Gupta, R.C., 1984. Relationships between order statistics and record values and some characterization results. J. Appl. Probab. 21, 425-430.
7. Huang, J.S., 1974. On a theorem of Ahsanullah and Rahman, J. Appl. Probab. 11, 216-218.
8. Huang, J.S., 1975. Characterization of distributions by the expected values of the order statistics. Ann. Inst. Statist. Math. 27, 87-93.
9. Huang, W.-J., Su, J.-C, 1994. On certain problems involving order statistics - a unified approach through order statistics property of point processes. Abstr. IMS Bull. 23, 400-401.
10. Kamps, U., 1992. Generalized Order Statistics. Habilitationsschrift, Aachen Uhiversity, Germany.
11. Kamps, U., 1995. A Concept of Generalized Order Statistics. Teubner, Stuttgart.
12. Kirmani, S.N.U.A., Beg, M.I., 1984. On characterization of distributions by expected records. Sankhyā A 46, 463-465.
13. Kotlarski, I., 1972. On a characterization of some distributions by conditional expectation. Sahkhyā A 34, 461-467.
14. Kotz, S., Shanbhag, D.N., 1980. Some new approaches to probability distributions. Adv. Appl. Probab. 12, 903-921.
15. Lin, G.D., Huang, J.S., 1987. A note on the sequence of expectations of maxima and of record values. Sankhyā A 49, 272-273.
16. Lin, G.D., 1989. Characterizations of distributions via moments of order statistics: a survey and comparison of methods. In: (Y. Dodge Ed.), Statistical Data Analysis and Inference, Elsevier, Amsterdam.
17. Nagaraja, H.N., 1977. On a characterization based on record values. Austral. J. Statist. 19, 70-73.
18. Nagaraja, H.N., 1986. Structure of discrete order statistics. J. Statist. Plann. Inference 13, 165-177.
19. Nagaraja, H.N., 1988a. Record values and related statistics - A review. Commun. Statist. Theor. Meth. 17, 2223-2238.
20. Nagaraja, H.N., 1988b. Some characterizations of continuous distributions based on regressions of adjacent order statistics and record values. Sankhyā A. 50, 70-73.
21. Nevzorov, V.B., 1987. Records. Probab. Theory Appl. 32, 201-228.
22. Nevzorov, V.B., 1992. A characterization of exponential distributions by correlations between records. Math. Meth. Statist. 1, 49-54.
23. Nevzorov, V.B., Stepanov, A.V., 1988, Records: the martingale approach to finding of moments. Rings and modules-Limit theorems of probab. theor. 2 Leningrad University 171-181, in Russian.
24. Rao, C.R., Shanbhag, D.N., 1986. Recent results on characterization of probability distributions: a unified approach through extensions of Deny's theorem. Adv. Appl. Probab. 18, 660-678.
25. Rao, C.R., Shanbhag, D.N., 1994. Choquet-Deny Type Functional Equations with Applications to Stochastic Models. Wiley, Chichester.
26. Shanbhag, D.N., 1970. Characterizations for exponential and geometric distributions. J. Amer. Statist. Assoc. 65, 1256-1259.
27. Shanbhag, D.N., 1977. An extension of the Rao-Rubin characterization. J. Appl. Probab. 14, 640-646.
28. Székely, G.J., Móri, T.F., 1985. An extremal property of rectangular distributions. Statist. Probab. Lett. 3, 107-109.