Matches in SemOpenAlex for { <https://semopenalex.org/work/W2015971566> ?p ?o ?g. }
Showing items 1 to 51 of
51
with 100 items per page.
- W2015971566 endingPage "317" @default.
- W2015971566 startingPage "315" @default.
- W2015971566 abstract "Let $X = (X_1, cdots, X_k)$ have the multinomial distribution, given by begin{equation*} tag{0.1} operatorname{Pr}{X = x} = n!prod^k_{i=1} (p^{xi}_i/(x_i!))end{equation*} where $x = (x_1, cdots, x_k), sum^k_{i=1} x_i = n$ and $sum^k_{i=1}p_i = 1$, and let begin{equation*} tag{0.2} C(p_1, cdots, p_m) = operatorname{Pr}{X_i geqq s_i; i = 1, cdots, m}end{equation*} where $sum^m_{i=1}s_ileqq n$ and $m leqq min (k - 1, n)$. We show that $C(p_1, cdots, p_m)$ is nondecreasing in $p_i$ for $i = 1, cdots, m$ and that for $s_i = s_j$, begin{equation*} tag{0.3} C(p_1, cdots, p_m) leqq C_{ij}(p_1, cdots, p_m)quadtext{and}end{equation*} begin{equation*} tag{0.4} C(p_1, cdots, p_m) geqq C_{ijt}(p_1, cdots, p_m)end{equation*} where $C_{ij}(p_1, cdots, p_m)$ is obtained from $C(p_1, cdots, p_m)$ by substituting $p = frac{1}{2}(p_i + p_j)$ for $p_i$ and $p_j$ and $C_{ijt}(p_1, cdots, p_m)$ is obtained from $C(p_1, cdots, p_m)$ by substituting $t$ for $p_i$ and $p_i + p_j - t$ for $p_j$ where $0 leqq t leqq min (p_i, p_j)$. These and similar results are shown. An application of these results to a multiple decision problem is indicated." @default.
- W2015971566 created "2016-06-24" @default.
- W2015971566 creator A5027178689 @default.
- W2015971566 date "1970-02-01" @default.
- W2015971566 modified "2023-10-12" @default.
- W2015971566 title "Monotonicity Properties of the Multinomial Distribution" @default.
- W2015971566 cites W2046284844 @default.
- W2015971566 doi "https://doi.org/10.1214/aoms/1177697211" @default.
- W2015971566 hasPublicationYear "1970" @default.
- W2015971566 type Work @default.
- W2015971566 sameAs 2015971566 @default.
- W2015971566 citedByCount "12" @default.
- W2015971566 countsByYear W20159715662014 @default.
- W2015971566 countsByYear W20159715662016 @default.
- W2015971566 crossrefType "journal-article" @default.
- W2015971566 hasAuthorship W2015971566A5027178689 @default.
- W2015971566 hasBestOaLocation W20159715661 @default.
- W2015971566 hasConcept C105795698 @default.
- W2015971566 hasConcept C114614502 @default.
- W2015971566 hasConcept C134306372 @default.
- W2015971566 hasConcept C192065140 @default.
- W2015971566 hasConcept C33923547 @default.
- W2015971566 hasConcept C72169020 @default.
- W2015971566 hasConceptScore W2015971566C105795698 @default.
- W2015971566 hasConceptScore W2015971566C114614502 @default.
- W2015971566 hasConceptScore W2015971566C134306372 @default.
- W2015971566 hasConceptScore W2015971566C192065140 @default.
- W2015971566 hasConceptScore W2015971566C33923547 @default.
- W2015971566 hasConceptScore W2015971566C72169020 @default.
- W2015971566 hasIssue "1" @default.
- W2015971566 hasLocation W20159715661 @default.
- W2015971566 hasLocation W20159715662 @default.
- W2015971566 hasOpenAccess W2015971566 @default.
- W2015971566 hasPrimaryLocation W20159715661 @default.
- W2015971566 hasRelatedWork W1979597421 @default.
- W2015971566 hasRelatedWork W2007980826 @default.
- W2015971566 hasRelatedWork W2061531152 @default.
- W2015971566 hasRelatedWork W2077600819 @default.
- W2015971566 hasRelatedWork W2808431411 @default.
- W2015971566 hasRelatedWork W2955220190 @default.
- W2015971566 hasRelatedWork W3002753104 @default.
- W2015971566 hasRelatedWork W4225152035 @default.
- W2015971566 hasRelatedWork W4245490552 @default.
- W2015971566 hasRelatedWork W4380682190 @default.
- W2015971566 hasVolume "41" @default.
- W2015971566 isParatext "false" @default.
- W2015971566 isRetracted "false" @default.
- W2015971566 magId "2015971566" @default.
- W2015971566 workType "article" @default.