Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T11:25:09.978Z Has data issue: false hasContentIssue false

Characterizations using record moments in a random record model and applications

Published online by Cambridge University Press:  14 July 2016

H. N. Nagaraja*
Affiliation:
Ohio State University
Gadi Barlevy*
Affiliation:
Northwestern University
*
Postal address: Department of Statistics, Ohio State University, 1958 Neil Avenue, Columbus, OH 43210-1247, USA. Email address: [email protected]
∗∗Current address: Economic Research Department, Federal Reserve Bank of Chicago, 230 South LaSalle Street, Chicago, IL 60604-1413, USA

Abstract

We consider a random record model from a continuous parent X with cumulative distribution function F, where the number of available observations is geometrically distributed. We show that, if E(|X|) is finite, then so is E(|Rn|) whenever Rn, the nth upper record value, exists. We prove that appropriately chosen subsequences of E(Rn) characterize F and subsequences of E(RnRn−1) identify F up to a location shift. We discuss some applications to the identification of wage-offer distributions in job search models.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 2003 

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

Arnold, B. C., Balakrishnan, N., and Nagaraja, H. N. (1998). Records. John Wiley, New York.CrossRefGoogle Scholar
Barlevy, G. (2002). Search capital and the wages of young men. Res. Rep., Department of Economics, Northwestern University.Google Scholar
Bunge, J., and Nagaraja, H. N. (1991). The distribution of certain record statistics from a random number of observations. Stoch. Process. Appl. 38, 167183.Google Scholar
Burdett, K., and Mortensen, D. (1998). Wage differentials, employer size, and unemployment. Internat. Econom. Rev. 39, 257273.Google Scholar
Gupta, R. C. (1984). Relationships between order statistics and record values and some characterization results. J. Appl. Prob. 21, 425430.CrossRefGoogle Scholar
Huang, J. S. (1975). Characterizations of distributions by the expected values of the order statistics. Ann. Inst. Statist. Math. 27, 8793.CrossRefGoogle Scholar
Kamps, U. (1998). Characterizations of distributions by recurrence relations and identities for moments of order statistics. In Handbook of Statistics, Vol. 16, Order Statistics: Theory and Methods, eds Balakrishnan, N. and Rao, C. R., Elsevier, Amsterdam, pp. 291311.Google Scholar
Kirmani, S. N. U. A., and Beg, M. I. (1984). On characterization of distributions by expected records. Sankhyā A 46, 463465.Google Scholar
Lin, G. D. (1988). Characterizations of distributions via relationships between two moments of order statistics. J. Statist. Planning Infer. 19, 7380.Google Scholar
Lin, G. D., and Huang, J. S. (1987). A note on the sequence of expectations of maxima and of record values. Sankhyā A 49, 272273.Google Scholar
Nagaraja, H. N. (1978). On the expected values of record values. Austral. J. Statist. 20, 176182.CrossRefGoogle Scholar