caa a22 4500 475826701 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1004148814661 doi (NATIONALLICENCE)springer-10.1023/A:1004148814661 Joint Distribution of Rises and Falls [Elektronische Daten] [James Fu, W.Y. Lou] The marginal distributions of the number of rises and the number of falls have been used successfully in various areas of statistics, especially in non-parametric statistical inference. Carlitz (1972, Duke Math. J. 39, 268-269) showed that the generating function of the joint distribution for the numbers of rises and falls satisfies certain complex combinatorial equations, and pointed out that he had been unable to derive the explicit formula for the joint distribution from these equations. After more than two decades, this latter problem remains unsolved. In this article, the joint distribution is obtained via the probabilistic method of finite Markov chain imbedding for random permutations. A numerical example is provided to illustrate the theoretical results and the corresponding computational procedures. The Institute of Statistical Mathematics, 2000 Eulerian and Simon Newcomb numbers nationallicence finite Markov chain imbedding nationallicence transition probability matrix nationallicence Fu James Department of Statistics, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada aut Lou W.Y. Department of Biomathematical Sciences, Mount Sinai School of Medicine, 10029-6574, New York, NY, U.S.A. aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 415-425 0020-3157 52:3<415 2000 52 10463 https://doi.org/10.1023/A:1004148814661 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004148814661 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fu James Department of Statistics, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada aut NATIONALLICENCE 700 1- Lou W.Y. Department of Biomathematical Sciences, Mount Sinai School of Medicine, 10029-6574, New York, NY, U.S.A aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 415-425 0020-3157 52:3<415 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer