Prediction of record values by using quantile regression curves and distortion functions

The purpose of the paper is to provide a general method based on conditional quantile curves to predict record values from preceding records. The predictions are based on conditional median (or median regression) curves. Moreover, conditional quantiles curves are used to provide confidence bands for these predictions. The method is based on the recently introduced concept of multivariate distorted distributions that are used instead of copulas to represent the dependence structure. This concept allows us to compute the conditional quantile curves in a simple way. The theoretical findings are illustrated with a non-parametric model (standard uniform), two parametric models (exponential and Pareto), and a non-parametric procedure for the general case. A real data set and a simulated case study in reliability are analysed.

Some Results on the Stress–Strength Reliability under the Distortion Functions

In this paper, the system reliability in a stress–strength model, when the distributions of the stress and the strength random variables are replaced by two distorted distributions, is considered. The conditions to increase the reliability under several distortion functions are studied. Furthermore, the changes in the residual stress–strength reliability, the mean remaining strength and the number of working components of a system are investigated when the original distributions have been affected by distortion functions. Some of the previous results in the literatures can be achieved as special cases of our results.

Stochastic comparisons and bounds for conditional distributions by using copula properties

We prove that different conditional distributions can be represented as distorted distributions. These representations are used to obtain stochastic comparisons and bounds for them based on properties of the underlying copula. These properties can be used to explain the meaning of mathematical properties of copulas connecting them with dependence concepts. Some applications and illustrative examples are provided as well.

STOCHASTIC COMPARISONS OF SYSTEMS BASED ON SEQUENTIAL ORDER STATISTICS VIA PROPERTIES OF DISTORTED DISTRIBUTIONS

We consider systems based on sequential order statistics (SOS) with underlying distributions possessing proportional hazard rates (PHRs). In that case, the lifetime distribution of the system can be expressed as a distorted distribution. Motivated by the distribution structure in the case of pairwise different model parameters, a particular class of distorted distributions, the generalized PHR model, is introduced and characterizations of stochastic comparisons for several stochastic orders are obtained. Moreover, results on the asymptotic behavior of some aging characteristics, for example, the hazard rate and the mean residual life function, of general distorted distributions as well as related bounds are given. The results are supplemented with limiting properties of the systems in the case of possibly equal model parameters. Some examples are presented in order to illustrate the application of the findings to systems based on SOS and also to systems with independent heterogeneous components.

Optical Tomography with Ultrasound Localization: Initial Clinical Results and Technical Challenges

Optical tomography with ultrasound localization utilizes co-registered ultrasound lesion structure information to guide optical imaging reconstruction. A hand-held probe consisting of a commercial ultrasound transducer and near infrared optical imaging sensors was used to simultaneously acquire ultrasound images and optical measurements. A dual-mesh scheme was used to map the ultrasound-visible lesions to finer-grid lesion regions and coarser-grid background regions for optical imaging reconstruction. As a result, optical imaging reconstruction was well-conditioned for inverse mapping of lesion hemoglobin concentration and blood oxygen saturation. Initial clinical results have shown that early stage invasive cancers may be distinguished by a two-fold greater total hemoglobin concentration compared with fibroadenomas and other benign lesions. Initial results of advanced cancers have shown that the hemoglobin distribution is highly distorted and heterogeneous and the distorted distributions correlate with histological microvessel density counts and could be used to assess chemotherapy response.