Abstract
The lower and upper record values obtained from sequences of independent and identically distributed [0, 1] random variables are discussed in this paper. Representations, in which record values are equal in distribution to sums and products of independent and identically distributed auxiliary random variables, are provided. Using these representations, distributional and moment characteristics of lower and upper record values taken from uniform samples are studied. Sequential sums of lower record values taken from samples of independent and uniformly distributed random variables are also discussed. The distributions and the Laplace transforms of the given sums are studied. The Laplace transform of the series of lower uniform record values are found. We also compared the sums of lower order statistics and record values which belong to a certain uniform sample.
Similar content being viewed by others
References
M. Ahsanullah and V. B. Nevzorov, Order Statistics. Examples and Exercises (Nova Sci., New York, 2005).
M. Ahsanullah and V. B. Nevzorov, Records via Probability Theory (Atlantis, Paris, 2015).
M. Ahsanullah, V. B. Nevzorov, and M. Shakil, An Introduction to Order Statistics (Atlantis Press, 2013).
B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records (Wiley, New York, 1998).
B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, A First Course in Order Statistics (Wiley, New York, 1992).
H. A. David and H. N. Nagaraja, Order Statistics, 3rd ed. (Wiley, New York, 2003).
V. B. Nevzorov, Records. Mathematical Theory (Fazis, Moscow, 2000) [in Russian]; V. B. Nevzorov, Translations of Mathematical Monographs (Am. Math. Soc., Providence, RI, 2001).
V. B. Nevzorov, “Representations of ordered random variables in the terms of sums or products of independent variables,” Vestn. St. Petersburg Univ.: Math. 49, 361–370 (2016). https://doi.org/10.3103/S1063454116040117
B. C. Arnold and J. A. Villasenor, “Progress on sums of records,” in Recent Developments in Ordered Random Variables, Ed. by M. Ahsanullah and M. Raqab (Nova Sci., New York, 2005), pp. 155–169.
Author information
Authors and Affiliations
Corresponding authors
About this article
Cite this article
Nevzorov, V.B., Stepanov, A.V. On Distributions of Sums of Record Values. Vestnik St.Petersb. Univ.Math. 52, 75–80 (2019). https://doi.org/10.3103/S1063454119010102
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1063454119010102