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Negative dependence structures through stochastic ordering.

Abdul-Hadi N. Ahmed (1990)

Trabajos de Estadística

Several new multivariate negative dependence concepts such as negative upper orthant dependent in sequence, negatively associated in sequence, right tail negatively decreasing in sequence and upper (lower) negatively decreasing in sequence through stochastic ordering are introduced. These concepts conform with the basic idea that if a set of random variables is split into two sets, then one is increasing whenever the other is decreasing. Our concepts are easily verifiable and enjoy many closure...

New results on the NBUFR and NBUE classes of life distributions

E. M. Shokry, A. N. Ahmed, E. A. Rakha, H. M. Hewedi (2009)

Applicationes Mathematicae

Some properties of the "new better than used in failure rate" (NBUFR) and the "new better than used in expectation" (NBUE) classes of life distributions are given. These properties include moment inequalities and moment generating functions behaviors. In addition, nonparametric estimation and testing of the survival functions of these classes are discussed.

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.

Note on the variance of the sum of Gaussian functionals

Marek Beśka (2010)

Applicationes Mathematicae

Let ( X i , i = 1 , 2 , . . . ) be a Gaussian sequence with X i ∈ N ( 0 , 1 ) for each i and suppose its correlation matrix R = ( ρ i j ) i , j ≥ 1 is the matrix of some linear operator R:l₂→ l₂. Then for f i ∈ L ² ( μ ) , i=1,2,..., where μ is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals f i ( X i ) , i=1,2,... .

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