Matches in SemOpenAlex for { <https://semopenalex.org/work/W1485265131> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W1485265131 endingPage "163" @default.
- W1485265131 startingPage "153" @default.
- W1485265131 abstract "<!-- *** Custom HTML *** --> We address a more general version of a classic question in probability theory. Suppose $bf {X sim N_p({mu},Sigma )}$. What functions of $bf {X}$ also have the $N_p({mu},Sigma )$ distribution? For $p = 1$, we give a general result on functions that cannot have this special property. On the other hand, for the $p = 2,3$ cases, we give a family of new nonlinear and non-analytic functions with this property by using the Chebyshev polynomials of the first, second and the third kind. As a consequence, a family of rational functions of a Cauchy-distributed variable are seen to be also Cauchy distributed. Also, with three i.i.d. $N(0,1)$ variables, we provide a family of functions of them each of which is distributed as the symmetric stable law with exponent $frac{1}{2}$. The article starts with a result with astronomical origin on the reciprocal of the square root of an infinite sum of nonlinear functions of normal variables being also normally distributed; this result, aside from its astronomical interest, illustrates the complexity of functions of normal variables that can also be normally distributed." @default.
- W1485265131 created "2016-06-24" @default.
- W1485265131 creator A5060515918 @default.
- W1485265131 creator A5061449196 @default.
- W1485265131 date "2004-01-01" @default.
- W1485265131 modified "2023-10-18" @default.
- W1485265131 title "Chebyshev polynomials and $G$-distributed functions of $F$-distributed variables" @default.
- W1485265131 cites W1987591432 @default.
- W1485265131 cites W2751862591 @default.
- W1485265131 doi "https://doi.org/10.1214/lnms/1196285387" @default.
- W1485265131 hasPublicationYear "2004" @default.
- W1485265131 type Work @default.
- W1485265131 sameAs 1485265131 @default.
- W1485265131 citedByCount "2" @default.
- W1485265131 countsByYear W14852651312013 @default.
- W1485265131 countsByYear W14852651312016 @default.
- W1485265131 crossrefType "book-chapter" @default.
- W1485265131 hasAuthorship W1485265131A5060515918 @default.
- W1485265131 hasAuthorship W1485265131A5061449196 @default.
- W1485265131 hasBestOaLocation W14852651312 @default.
- W1485265131 hasConcept C111472728 @default.
- W1485265131 hasConcept C114614502 @default.
- W1485265131 hasConcept C118615104 @default.
- W1485265131 hasConcept C121332964 @default.
- W1485265131 hasConcept C129785596 @default.
- W1485265131 hasConcept C134306372 @default.
- W1485265131 hasConcept C138885662 @default.
- W1485265131 hasConcept C158622935 @default.
- W1485265131 hasConcept C189950617 @default.
- W1485265131 hasConcept C202444582 @default.
- W1485265131 hasConcept C2777742833 @default.
- W1485265131 hasConcept C33923547 @default.
- W1485265131 hasConcept C41895202 @default.
- W1485265131 hasConcept C49344536 @default.
- W1485265131 hasConcept C62520636 @default.
- W1485265131 hasConceptScore W1485265131C111472728 @default.
- W1485265131 hasConceptScore W1485265131C114614502 @default.
- W1485265131 hasConceptScore W1485265131C118615104 @default.
- W1485265131 hasConceptScore W1485265131C121332964 @default.
- W1485265131 hasConceptScore W1485265131C129785596 @default.
- W1485265131 hasConceptScore W1485265131C134306372 @default.
- W1485265131 hasConceptScore W1485265131C138885662 @default.
- W1485265131 hasConceptScore W1485265131C158622935 @default.
- W1485265131 hasConceptScore W1485265131C189950617 @default.
- W1485265131 hasConceptScore W1485265131C202444582 @default.
- W1485265131 hasConceptScore W1485265131C2777742833 @default.
- W1485265131 hasConceptScore W1485265131C33923547 @default.
- W1485265131 hasConceptScore W1485265131C41895202 @default.
- W1485265131 hasConceptScore W1485265131C49344536 @default.
- W1485265131 hasConceptScore W1485265131C62520636 @default.
- W1485265131 hasLocation W14852651311 @default.
- W1485265131 hasLocation W14852651312 @default.
- W1485265131 hasLocation W14852651313 @default.
- W1485265131 hasOpenAccess W1485265131 @default.
- W1485265131 hasPrimaryLocation W14852651311 @default.
- W1485265131 hasRelatedWork W170218341 @default.
- W1485265131 hasRelatedWork W1978042415 @default.
- W1485265131 hasRelatedWork W1989633850 @default.
- W1485265131 hasRelatedWork W2017331178 @default.
- W1485265131 hasRelatedWork W2020174565 @default.
- W1485265131 hasRelatedWork W2056791101 @default.
- W1485265131 hasRelatedWork W2736223503 @default.
- W1485265131 hasRelatedWork W3013626938 @default.
- W1485265131 hasRelatedWork W3086542228 @default.
- W1485265131 hasRelatedWork W4253170791 @default.
- W1485265131 isParatext "false" @default.
- W1485265131 isRetracted "false" @default.
- W1485265131 magId "1485265131" @default.
- W1485265131 workType "book-chapter" @default.