zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A sequential procedure for deciding among three hypotheses. (English) Zbl 0816.62065

Summary: Abraham Wald developed the Sequential Probability Ratio Test in the 1940’s to perform simple vs. simple hypothesis tests that would control both Type I and Type II error rates. Some applications require a test of three hypotheses. In addition, to perform a simple vs. composite two- sided test, a three-hypotheses test with all hypotheses simple has been suggested. Methods have been proposed that will test three hypotheses sequentially. They range widely in simplicity and accuracy.

In this paper, approximate probabilities of error for Armitage’s test are derived. A method of adjusting the error rates used to establish the decision boundaries in order to attain the nominal error rates is developed. The procedure is compared to existing ones by Monte-Carlo simulation.

MSC:
62L10Sequential statistical analysis