A criterion for comparability of weighted densities

Journal of Inequalities and Applications

In this paper we study inequalities between weighted densities of sets of natural numbers corresponding to different weight functions. Depending on the asymptotic relation between the weight functions, we give sharp bounds for possible values of one density when the values of another density are given. In particular, we give a condition for two weight functions to generate equivalent weighted densities.

Journal of Statistical Planning and Inference, 2003

For one-parameter natural exponential and power series families we give some general characterizations from an a ne relation connecting the mean of member distributions and their length biased versions. Examples subsume many known cases. Other characterizations are explored using random variable relations involving the length biased version of partial sums. Finally, characterizations of the law of X admitting more general weights are obtained by equating the laws of a function H (X ) and the weighted version of X .

2017

New concepts on fractional probability theory are introduced and some inequalities for the fractional weighted expectation and the fractional weighted variance of continuous random variables are obtained. Other fractional results related to the two orders-fractional % weighted moment are also established. Some recent results on integral inequality theory can be deduced as some special cases. At the end, some applications on the uniform random variable are given.

Journal of Statistical Planning and Inference, 1999

In this paper, some partial ordering results regarding the original and the weighted distributions of random variables and random vectors have been derived. Bivariate weighted distributions have been discussed and some results have been obtained regarding them. Some dependence properties have also been studied.

Probability in the Engineering and Informational Sciences, 1987

For nonnegative random variables, the weighted distributions have been compared with the original distributions with the help of partial orderings of probability distributions. Bounds on the moments of the weighted distributions have been obtained in terms of the moments of the original distributions for some nonparametric classes of aging distributions.

Information Sciences, 2009

In the paper relations between weighted asymptotic fuzzy measures determined by weights n p ; p 2 ½À1; 1Þ are investigated. Some previously published results are improved and a conjecture on possibility of simultaneous prescription of the values of these measures for two values of parameters is proved.

We prove the convergence of weighted sums of associated random variables normalized by n 1/p , p ∈ (1, 2), assuming the existence of moments somewhat larger than p, depending on the behaviour of the weights, improving on previous results by getting closer to the moment assumption used for the case of constant weights. Besides moment conditions, we assume a convenient behaviour either on truncated covariances or on joint tail probabilities. Our results extend analogous characterizations known for sums of independent or negatively dependent random variables.

Entropy, 2020

In this paper, various stochastic ordering properties of a parametric family of weighted distributions and the associated mixture model are developed. The effect of stochastic variation of the output random variable with respect to the parameter and/or the underlying random variable is specifically investigated. Special weighted distributions are considered to scrutinize the consistency as well as the usefulness of the results. Stochastic comparisons of coherent systems made of identical but dependent components are made and also a result for comparison of Shannon entropies of weighted distributions is developed.

Statistics & Probability Letters, 2014

The Fisher information on θ of the r-size weighted pdf f r (x; θ) and its parent pdf f (x; θ) are compared leading to some characterization properties for f (x; θ). Additionally, some bounds for the Fisher information in terms of r are also presented.

In this note, some fundamental results including relationship be-tween weighted distribution functions and mean advantage over inferi-ors functions are established. Ordering of reliability and/or distribution functions via mean advantage over inferiors functions and related func-tions for parent and weighted reliability functions are presented. Some applications and examples are given.