One-Sided Confidence Contours for Probability Distribution Functions
Birnbaum, Z. W. ; Tingey, Fred H.
Ann. Math. Statist., Tome 22 (1951) no. 4, p. 592-596 / Harvested from Project Euclid
Let $F(x)$ be the continuous distribution function of a random variable $X,$ and $F_n(x)$ the empirical distribution function determined by a sample $X_1, X_2, \cdots, X_n$. It is well known that the probability $P_n(\epsilon)$ of $F(x)$ being everywhere majorized by $F_n(x) + \epsilon$ is independent of $F(x)$. The present paper contains the derivation of an explicit expression for $P_n(\epsilon)$, and a tabulation of the 10%, 5%, 1%, and 0.1% points of $P_n(\epsilon)$ for $n =$ 5, 8, 10, 20, 40, 50. For $n =$ 50 these values agree closely with those obtained from an asymptotic expression due to N. Smirnov.
Publié le : 1951-12-14
Classification: 
@article{1177729550,
     author = {Birnbaum, Z. W. and Tingey, Fred H.},
     title = {One-Sided Confidence Contours for Probability Distribution Functions},
     journal = {Ann. Math. Statist.},
     volume = {22},
     number = {4},
     year = {1951},
     pages = { 592-596},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177729550}
}
Birnbaum, Z. W.; Tingey, Fred H. One-Sided Confidence Contours for Probability Distribution Functions. Ann. Math. Statist., Tome 22 (1951) no. 4, pp.  592-596. http://gdmltest.u-ga.fr/item/1177729550/