| V.I. Norkin and N.V. Roenko, ff-Concave Functions and Measures and Their Applications. Kibernet. Sistem. Anal. 189 (1991) 77--88 (in Russian); translation in: Cybernet. Systems Anal. 27 (1991) 860--869. |
....approach that generates them only when needed. We end this section with sufficient conditions for the r concavity of the joint distribution function in the case of integer valued independent components. Our assertion, presented in the next proposition is the discrete version of an observation from [11]. Proposition 3.4. Assume that the components i of , i = 1; s, are independent, and that the marginal distribution functions F i are r i concave on sets A i ae ZZ. i) If r i 0, i = 1; s, then F is r concave on A = A 1 Theta Delta Delta Delta Theta A s with r = P s ....
V.I. Norkin and N.V. Roenko, ff-Concave Functions and Measures and Their Applications. Kibernet. Sistem. Anal. 189 (1991) 77--88 (in Russian); translation in: Cybernet. Systems Anal. 27 (1991) 860--869.
....approach that generates them only when needed. We end this section with sufficient conditions for the r concavity of the joint distribution function in the case of integer valued independent components. Our assertion, presented in the next proposition is the discrete version of an observation from [11]. Proposition 3.4 Assume that the components i of , i = 1; s, are independent, and that the marginal distribution functions F i are r i concave on sets A i ae ZZ. i) If r i 0, i = 1; s, then F is r concave on A = A 1 Theta Delta Delta Delta Theta A s with r = P s ....
V.I. Norkin and N.V. Roenko, ff-Concave Functions and Measures and Their Applications. Kibernet. Sistem. Anal. 189 (1991) 77--88 (in Russian); translation in: Cybernet. Systems Anal. 27 (1991) 860--869.
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