Distribution of Sample Arrangements for Runs Up and Down
Olmstead, P. S.
Ann. Math. Statist., Tome 17 (1946) no. 4, p. 24-33 / Harvested from Project Euclid
Using the notation of Levene and Wolfowitz [1], a new recursion formula is used to give the exact distribution of arrangements of $n$ numbers, no two alike, with runs up or down of length $p$ or more. These are tabled for $n$ and $p$ through $n = 14$. An exact solution is given for $p \geq n/2$. The average and variance determined by Levene and Wolfowitz are presented in a simplified form. The fraction of arrangements of $n$ numbers with runs of length $p$ or more are presented for the exact distributions, for the limiting Poisson Exponential, and for an extrapolation from the exact distributions. Agreement among the tables is discussed.
Publié le : 1946-03-14
Classification: 
@article{1177731019,
     author = {Olmstead, P. S.},
     title = {Distribution of Sample Arrangements for Runs Up and Down},
     journal = {Ann. Math. Statist.},
     volume = {17},
     number = {4},
     year = {1946},
     pages = { 24-33},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177731019}
}
Olmstead, P. S. Distribution of Sample Arrangements for Runs Up and Down. Ann. Math. Statist., Tome 17 (1946) no. 4, pp.  24-33. http://gdmltest.u-ga.fr/item/1177731019/