1970/09/01 by Erling B. Andersen · 11 citations
Mathematics · #Approximation Theory and Sequence Spaces #Fixed Point Theorems Analysis #Exponential family #Mathematics #Sufficient statistic #Statistic #Sample space #Order statistic #Range (aeronautics) #Exponential function #Property (philosophy) #Sample (material) #Space (punctuation) #Applied mathematics #Type (biology) #Pure mathematics #Discrete mathematics #Statistics #Mathematical analysis #Computer science
paper · doi:10.2307/2284291
published in Journal of the American Statistical Association 65(331), 1248
openalex publication_date 1970/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
All known theorems of the Darmois-Koopman-Pitman type are based on the assumption of absolutely continuous probabilities. In this article, a Darmois-Koopman-Pitman type theorem is proved for families of probability measures that are defined on discrete sample spaces. Two assumptions are imposed on the sufficient statistic for the family: (1) the range space of the sufficient statistic can be completely ordered, and (2) this ordering of the range space of the sufficient statistic has a certain regularity property. Under (1) and (2), it can be proved that the given family is exponential of order 1.