Further development of an open problem.
Further results on the generalized cumulative entropy
Recently, a new concept of entropy called generalized cumulative entropy of order was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived...
Gaussian Approximation of Moments of Sums of Independent Random Variables
We continue the research of Latała on improving estimates of the pth moments of sums of independent random variables with logarithmically concave tails. We generalize some of his results in the case of 2 ≤ p ≤ 4 and present a combinatorial approach for even moments.
Gaussian maximum of entropy and reversed log-Sobolev inequality
General proportional mean residual life model
By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and aging classes...
Generalized Bell polynomials and the combinatorics of Poisson central moments.
Generalized Binomial law and Regularly Varying Moments
Generalized convolutions II
Generalized convolutions III
Generalized convolutions IV
Generalized convolutions V
Generalized covariance inequalities
We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.
Generalized distributions of order associated with success runs in Bernoulli trials.
Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples.
Generalized Gauss-Chebyshev Inequalities for Unimodal Distributions.
Generalized Levy representation of norms and isometric embeddings into -spaces
Generalized normal distributions.
It is well known (see [2], p. 158) that if X and Y are independent random variables with a continuous joint probability density function (pdf) which is spherically symmetric about the origin, then both X and Y are normally distributed. In this note we examine the condition that the joint pdf be spherically symmetric about the origin and show that the normal distribution is strongly dependent on the choice of metric for R2.
Generalized tempered stable processes
This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy processes are...
Generating Dirichlet random vectors using a rejection property
Geometric infinite divisibility, stability, and self-similarity: an overview
The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of components for each p ∈ (0,1), where is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric stable....