Distribution functions and log-concavity
Identifieur interne : 001416 ( PascalFrancis/Checkpoint ); précédent : 001415; suivant : 001417Distribution functions and log-concavity
Auteurs : H. Finner [Allemagne] ; M. RotersSource :
- Communications in statistics. Theory and methods [ 0361-0926 ] ; 1993.
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- Pascal (Inist)
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Abstract
This paper presents a collection of log-concavity results of one-dimensional cumulative distribution functions (cdf's) F(x, ) and the related functions F(x, ) = 1 - F(x, ), Jc(x, ) = F(x + c, ) - F(x, ), c >0, in both x ∈ R or x ∈ Z and ∈ Θ, where R denotes the real line and Z the set of integers. We give a review of results available in the literature and try to fill some gaps in this field. It is well-known that log-concavity properties in x of a density f carry over to F. F. and Jc in the continuous and discrete case. In addition, it will be seen that the log-concavity of g(y) = f(ey) in y for a Lebesgue density f with f(x) = 0 for x < 0 implies the log-concavity of F
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Trier, FB IV mathematik/statistik</s1><s2>W-5500 Trier</s2><s3>DEU</s3></inist:fA14><country>Allemagne</country><wicri:noRegion>W-5500 Trier</wicri:noRegion><wicri:noRegion>FB IV mathematik/statistik</wicri:noRegion><wicri:noRegion>W-5500 Trier</wicri:noRegion></affiliation></author><author><name sortKey="Roters, M" sort="Roters, M" uniqKey="Roters M" first="M." last="Roters">M. Roters</name></author></analytic><series><title level="j" type="main">Communications in statistics. Theory and methods</title><title level="j" type="abbreviated">Commun. stat., Theory methods</title><idno type="ISSN">0361-0926</idno><imprint><date when="1993">1993</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Communications in statistics. Theory and methods</title><title level="j" type="abbreviated">Commun. stat., Theory methods</title><idno type="ISSN">0361-0926</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Convexity</term><term>Convolution</term><term>Distribution function</term><term>Inequality</term><term>Probability</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Fonction répartition</term><term>Probabilité</term><term>Inégalité</term><term>Convolution</term><term>Convexité</term><term>Fonction Polya</term><term>Positivité totale</term><term>Fonction log concave</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">This paper presents a collection of log-concavity results of one-dimensional cumulative distribution functions (cdf's) F(x, ) and the related functions F(x, ) = 1 - F(x, ), J<sub>c</sub>(x, ) = F(x + c, ) - F(x, ), c >0, in both x ∈ R or x ∈ Z and ∈ Θ, where R denotes the real line and Z the set of integers. We give a review of results available in the literature and try to fill some gaps in this field. It is well-known that log-concavity properties in x of a density f carry over to F. F. and J<sub>c</sub> in the continuous and discrete case. In addition, it will be seen that the log-concavity of g(y) = f(e<sup>y</sup>) in y for a Lebesgue density f with f(x) = 0 for x < 0 implies the log-concavity of F</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0361-0926</s0></fA01><fA02 i1="01"><s0>CSTMDC</s0></fA02><fA03 i2="1"><s0>Commun. stat., Theory methods</s0></fA03><fA05><s2>22</s2></fA05><fA06><s2>8</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Distribution functions and log-concavity</s1></fA08><fA11 i1="01" i2="1"><s1>FINNER (H.)</s1></fA11><fA11 i1="02" i2="1"><s1>ROTERS (M.)</s1></fA11><fA14 i1="01"><s1>Univ. 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Roters</name></noCountry><country name="Allemagne"><noRegion><name sortKey="Finner, H" sort="Finner, H" uniqKey="Finner H" first="H." last="Finner">H. Finner</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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