Extreme order statistics on Galton-Watson trees

Anthony G. Pakes

doi:10.1007/bf02742867

journal article Jan 01, 1998

Extreme order statistics on Galton-Watson trees

Anthony G. Pakes

Metrika Vol. 47 No. 1 pp. 95-117 · Springer Science and Business Media LLC

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References

22

[1]

Arnold BC, Villaseñor JA (1996) The tallest man in the world. In: Nagaraja HN, Sen PK, Morrison DF (eds.) Statistical Theory and Applications. Papers in Honor of Herbert A. David, Springer, New York, pp. 81–88 10.1007/978-1-4612-3990-1_8

[2]

Athreya KB, Ney PE (1972) Branching processes. Springer-Verlag, Berlin 10.1007/978-3-642-65371-1

[3]

Bingham NH, Doney RA (1974) Asymptotic properties of super-critical branching processes. I: The Galton-Watson process. Adv. Appl. Prob. 6: 711–731 10.2307/1426188

[4]

Bru B, Jongmans F, Seneta E (1992) I.J. Bienaymé: Family information and proof of the criticality theorem. Intl. Statist. Review 60: 177–183 10.2307/1403648

[5]

de Meyer A (1982) On a theorem of Bingham and Doney. J. Appl. Prob. 19: 217–220 10.2307/3213931

[6]

David HA (1981) Order statistics, 2nd ed. Wiley, New York

[7]

Galambos J (1978) The asymptotic theory of extreme order statistics. Wiley, New York

[8]

Guttorp P (1991) Statistical inference for branching processes. Wiley, New York

[9]

Guttorp P (1995) Three papers on the history of branching processes. Intl. Statist. Review 63: 233–245

[10]

Harris TE (1951) Some mathematical models for branching processes. In: Neyman J (ed.) Second Symposium on Probability and Statistics, University of California Press, Berkeley, pp. 305–328

[11]

Jagers P (1975) Branching processes with biological applications. Wiley, London

[12]

Kaplan N (1983) The limiting behaviour of record values for an increasing population. Unpublished report, Dept. Statistics, Univ California, Berkeley

[13]

Pakes AG (1971) Some limit theorems for the total progeny of a branching process. Adv. Appl. Prob. 3: 176–192 10.2307/1426333

[14]

Pakes AG (1974) Some limit theorems for Markov chains with applications to branching processes. In: Williams EJ (ed.) Studies in Probability and Statistics, North-Holland, Amsterdam, pp. 21–39

[15]

Pakes AG (1983) Remarks on a model of competitive bidding for employment. J. Appl. Prob. 20: 349–357 10.2307/3213807

[16]

Pakes AG (1998) A limit theorem for the maxima of the para-critical simple branching process. Adv. Appl. Prob., To appear 10.1239/aap/1035228127

[17]

Pakes AG (1997) Revisiting conditional limit theorems for the mortal simple branching process. Bernoulli, submitted

[18]

Papangelou F (1968) A lemma on the Galton-Watson process and some of its consequences. Proc. Amer. Math. Soc. 19: 1169–1179 10.1090/s0002-9939-1968-0232457-5

[19]

Phatarfod RP (1983) Private communication

[20]

Resnick S (1987) Extreme values, regular variation, and point processes. Springer-Verlag, New York 10.1007/978-0-387-75953-1

[21]

Slack RS (1968) A branching process with mean one and possibly infinite variance. Z. Wahrs. 9: 139–145 10.1007/bf01851004

[22]

Yang MCK (1975) On the increasing distribution of the inter-record times in an increasing population. J. Appl. Prob. 12: 148–154 10.2307/3212417

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Published: Jan 01, 1998
Vol/Issue: 47(1)
Pages: 95-117
License: View

Authors

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Anthony G. Pakes

Cite This Article

Anthony G. Pakes (1998). Extreme order statistics on Galton-Watson trees. Metrika, 47(1), 95-117. https://doi.org/10.1007/bf02742867

Extreme order statistics on Galton-Watson trees

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