Simple random walk statistics. Part I: Discrete time results
1996 ◽
Vol 33
(02)
◽
pp. 311-330
◽
Keyword(s):
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.
Keyword(s):
1967 ◽
Vol 38
(4)
◽
pp. 1042-1053
◽
Keyword(s):
Keyword(s):
1990 ◽
Vol 24
(1)
◽
pp. 119-133
◽
Keyword(s):
1996 ◽
Vol 33
(02)
◽
pp. 331-339
◽
Keyword(s):
1972 ◽
Vol 23
(2)
◽
pp. 276-287
◽
Keyword(s):
1985 ◽
Vol 12
◽
pp. 177-191
◽