Monotonicity of ratios involving incomplete gamma functions with actuarial applications.
Mouvement brownien et inégalité de Hardy dans
Multivariate Gamma Distributions with One-Factorial Accompanying Correlation Matrices and Applications to the Distribution of the Multivariate Range.
Negative dependence structures through stochastic ordering.
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...
Negatively dependent bounded random variable probability inequalities and the strong law of large numbers.
New continuity estimates of geometric sums.
New results on the NBUFR and NBUE classes of life distributions
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.
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 dispersion of .
Note on Dispersion of Xalpha
Note on the multidimensional Gebelein inequality
We generalize the Gebelein inequality for Gaussian random vectors in .
Note on the variance of the sum of Gaussian functionals
Let be a Gaussian sequence with for each i and suppose its correlation matrix is the matrix of some linear operator R:l₂→ l₂. Then for , i=1,2,..., where μ is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals , i=1,2,... .
Note sur quelques inégalités entre les valeurs probables d'une grandeur aléatoire qui ne prend que des valeurs positives
Notes on Qi type integral inequalities.
On a multivariate version of Bernstein's inequality.
On an exponential inequality and a strong law of large numbers for monotone measures
An exponential inequality for Choquet expectation is discussed. We also obtain a strong law of large numbers based on Choquet expectation. The main results of this paper improve some previous results obtained by many researchers.
On an inequality and the related characterization of the gamma distribution
In this paper we derive conditions upon the nonnegative random variable under which the inequality holds for a fixed nonnegative constant and for any absolutely continuous function . Taking into account the characterization of a Gamma distribution we consider the functional and establishing some of its properties we show that and that iff the random variable has a Gamma distribution.
On an inequality of P. Erdös, J. Neveu, A. Rényi and S. Zubrzycki
On concentration of self-bounding functions.
On ℝd-valued peacocks
In this paper, we consider ℝd-valued integrable processes which are increasing in the convex order, i.e. ℝd-valued peacocks in our terminology. After the presentation of some examples, we show that an ℝd-valued process is a peacock if and only if it has the same one-dimensional marginals as an ℝd-valued martingale. This extends former results, obtained notably by Strassen [Ann. Math. Stat. 36 (1965) 423–439], Doob [J. Funct. Anal. 2 (1968) 207–225] and Kellerer [Math. Ann. 198 (1972) 99–122].