Yolanda del Águila

Multivariate weighted distributions: a review and some extensions

We study some properties for multivariate weighted distributions related to reliability measures, ordering, characterization and dependence properties, by compiling and extending previous results given by different authors. We pay special attention to the multivariate size biased and equilibrium distributions, and propose a new definition for the multivariate equilibrium distribution.

Characterizations using weighted distributions

For one-parameter natural exponential and power series families we give some general characterizations from an affine 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.

Parametric Estimation from Weighted Samples

In this paper we obtain parameter estimators based on length (size) biased samples for different models. We compare the estimators and Fishers information from usual samples and length biased samples. Moreover, we obtain the estimators based on two samples, one unbiased and another one biased. We obtain a similar study for samples from a renewal process.

Characterizations and ordering properties based on log-odds functions

In this paper, we obtain some general results on characterizations of probability distributions from relationships between conditional moment, failure rate, and log-odds rate functions. We also study stochastic orders and classes based on the log-odds rate function and some relationships with usual stochastic orderings and classes. Some characterizations and ordering properties are obtained by using weighted distributions.