Generalized random walk and distributions of some rank order statistics

In a famous paper, Dwass (1967) proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows us to extend Dwass's results in several ways, namely arbitrary endpoints, horizontal steps and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process.

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Random Walk and Distributions of Rank Order Statistics

SIAM Journal on Applied Mathematics ◽

10.1137/0123029 ◽

1972 ◽

Vol 23 (2) ◽

pp. 276-287 ◽

Cited By ~ 8

Author(s):

K. G. Aneja ◽

Kanwar Sen

Keyword(s):

Random Walk ◽

Order Statistics ◽

Rank Order ◽

Rank Order Statistics

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Simple random walk statistics. Part I: Discrete time results

Journal of Applied Probability ◽

10.1017/s0021900200099745 ◽

1996 ◽

Vol 33 (02) ◽

pp. 311-330 ◽

Cited By ~ 1

Author(s):

W. Katzenbeisser ◽

W. Panny

Keyword(s):

Random Walk ◽

Random Walks ◽

Order Statistics ◽

Discrete Time ◽

Rank Order ◽

Simple Random Walk ◽

Alternative Method ◽

Starting Point ◽

Famous Paper ◽

Rank Order Statistics

In a famous paper, Dwass (1967) proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows us to extend Dwass's results in several ways, namely arbitrary endpoints, horizontal steps and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process.

Download Full-text