References
Anscombe, F. J. (1952). Large-sample theory of sequential estimation,Proc. Camb. Phil. Soc.,48, 600.
Barndorff-Nielson, O. (1964). On the limit distribution of the maximum of a random number of independent random variables,Acta Math. Acad. Sci. Hung. 15, 399–403.
Blum, J. R., Hanson, D. L. and Rosenblatt, J. I. (1963). On the central limit theorem for the sum of a random number of independent random variables,Zeit. Wahrscheinlichkeitsth.,1, 389–393.
Chung, K. L. (1948). Asymptotic distribution of the maximum cumulative sum of independent random variables,Bul. Amer. Math. Soc.,54, 1162–1170.
Erdös, P. and Kac, M. (1946) On certain limit theorems of the theory of probability,Bull. Amer. Math. Soc.,52, 292–302.
Mogyoródi, J. (1962). A central limit theorem for the sum of a random number of independent random variables,Publ. Math. Inst. Hung. Acad. Sci., Series A,7, 409–424.
Mogyoródi, J. (1966). A remark on stable sequences of random variables and a limit distribution theorem for a random sum of independent random variables,Acta Math. Acad. Sci. Hung.,17, 401–409.
Puri, P. S. (1972). On the asymptotic distribution of the maximum of sums of a random number of I.I.D. random variables,Mimeograph Series, No. 272, Dept. of Statistics, Purdue University.
Rényi, A. (1957). On the asymptotic distribution of the sum of a random number of independent random variables,Acta Math. Acad. Sci. Hung.,8, 193–199.
Rényi, A. (1958). On mixing sequences of sets,Acta Math. Acad. Sci. Hung.,9, 215–228.
Rényi, A. (1960). On the central limit theorem for the sum of a random number of independent random variables,Acta Math. Acad. Sci. Hung.,11, 97–102.
Spitzer, F. (1956). A combinatorial lemma and its application to probability theory,Trans. Amer. Math. Soc.,82, 323–339.
Sreehari, M. (1968). A limit theorem for the maximum of cumulative sums,Acta Math. Acad. Sci. Hung.,19, 117–120.
Takács, L. (1970). On the distribution of the maximum of sums of mutually independent and identically distributed random variables,Advances Appl. Prob.,2, 344–354.
Author information
Authors and Affiliations
Additional information
This investigation was supported in part by research grant GM-10525 from NIH, Public Health Service, at the University of California, Berkeley
About this article
Cite this article
Puri, P.S. On the asymptotic distribution of the maximum of sums of a random number of I.I.D. random variables. Ann Inst Stat Math 29, 77–87 (1977). https://doi.org/10.1007/BF02532776
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02532776