Nuria Torrado

On Stochastic Comparisons of Largest Order Statistics in the Scale Model

Let be independent non negative random variables with , i = 1, …, n, where λi > 0, i = 1, …, n and F is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic Xλn: n is smaller than another one Xθn: n according to likelihood ratio ordering. Furthermore, we apply these results when F is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases.

Comparisons between largest order statistics from multiple-outlier models

In this work, we discuss stochastic comparisons between the largest order statistics from multiple-outlier models when the numbers of independent and identically distributed random variables are different. That is, if is the largest order statistic among and is the largest order statistic among , where and , we discuss whether and are ordered in some stochastic sense.

Likelihood ratio order of spacings from two heterogeneous samples

In this article we obtain some new results in the area of stochastic comparisons of simple and normalized spacings from two samples of heterogeneous exponential random variables. Specifically, we investigate conditions under which successive spacings are ordered in the likelihood ratio ordering. We also show some applications of our results to the multiple-outlier case.

Software Reliability Modeling with Software Metrics Data via Gaussian Processes

In this paper, we describe statistical inference and prediction for software reliability models in the presence of covariate information. Specifically, we develop a semiparametric, Bayesian model using Gaussian processes to estimate the numbers of software failures over various time periods when it is assumed that the software is changed after each time period and that software metrics information is available after each update. Model comparison is also carried out using the deviance information criterion, and predictive inferences on future failures are shown. Real-life examples are presented to illustrate the approach.

On the conjecture of Kochar and Korwar

In this article, we partially solve a conjecture by Kochar and Korwar (1996) [9] in relation to the normalized spacings of the order statistics of a sample of independent exponential random variables with different scale parameters. In the case of a sample of size n=3, they proved the ordering of the normalized spacings and conjectured that result holds for all n. We prove this conjecture for n=4 for both spacings and normalized spacings and generalize some results to n>4.

Stochastic comparisons between extreme order statistics from scale models

ABSTRACT Stochastic ordering relations between extreme order statistics from exponential, Weibull and gamma distributions have been studied extensively by many researchers in recent years. In this work, we obtain various ordering results for the comparisons of two extreme order statistics from scale models when one set of scale parameters majorizes the other. The new results obtained here are applied when the baseline distributions are exponentiated Weibull or generalized gamma distributions. In this way, we generalize and extend some results established recently in the literature.

Sample Spacings with Applications in Multiple-Outlier Models

The difference between successive order statistics is denoted as spacing in the literature. They appear in reliability theory, survival analysis, and systems engineering where the times between failures of components of a system correspond with the spacings associated with order statistics. The purpose of this work is to survey the literature about stochastic comparisons of spacings from one and two sequences of order statistics.

Likelihood ratio comparisons among spacings related to both one or two samples

In this paper, we investigate some stochastic comparisons in terms of likelihood ratio ordering between spacings from independent random variables exponentially distributed with different scale parameters. We partially solve some open problems in [Wen S, Lu Q, Hu T. Likelihood ratio orderings of spacings of heterogeneous exponential random variables. J Multivariate Anal. 2007;98:743–756] for a one-sample problem and in [Hu T, Lu Q, Wen S. Stochastic comparisons and dependence of spacings from two samples of exponential random variables. Commun Stat – Theory Methods 2006;35:979–988] for a two-sample problem. Specifically, we prove that the second spacing is always smaller than the third spacing in terms of the likelihood ratio order and we provide the ordering among all spacings in the case n=4. In the two-sample case, we establish comparisons between the second spacings related to each sample under certain conditions.