Rényi’s residual entropy: A quantile approach

In the present paper, we introduce a quantile based Rényi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Rényi’s entropy function, the quantile version uniquely determines the distribution

Absolute risk of breast cancer for Australian women with a family history

Background: The purpose of the present paper was to estimate the absolute risk of breast cancer over the remainder of a lifetime in Australian women with different categories of family history. Methods: Age-specific breast cancer incidence rates were adjusted for screening effects, and rates in those with no family history were estimated using the attributable fraction (AF). Relative risks from a published meta-analysis were applied to obtain incidence rates for different categories of family history, and age-specific incidence was converted to cumulative risk of breast cancer. The risk estimates were based upon Australian population statistics and published relative risks. Breast cancer incidence was from New South Wales women for 1996. The AF was calculated using prevalence of a family history of breast cancer from data on Queensland women. The cumulative absolute risk of breast cancer was calculated from decade and mid-decade ages to age 79 years, not adjusted for competing causes of death. Results: Lifetime risk is approximately 8.6% (1 in 12) for the general population and 7.8% (1 in 13) for those without a family history. Women with one relative affected have lifetime risks of 1 in 6-8 and those with two relatives affected have lifetime risks of 1 in 4-6. The cumulative residual lifetime risk decreases with advancing age; by age 60 years all groups with only one relative affected have well above a 90% probability of not developing breast cancer to age 79 years. Conclusions: These Australian risk statistics are useful for public information and in the clinical setting. Risks given here apply to women with average breast cancer risk from other risk factors.

Quantile based entropy function

Quantile functions are efficient and equivalent alternatives to distribution functions in modeling and analysis of statistical data (see Gilchrist, 2000; Nair and Sankaran, 2009). Motivated by this, in the present paper, we introduce a quantile based Shannon entropy function. We also introduce residual entropy function in the quantile setup and study its properties. Unlike the residual entropy function due to Ebrahimi (1996), the residual quantile entropy function determines the quantile density function uniquely through a simple relationship. The measure is used to define two nonparametric classes of distributions

Some Results on Reciprocal Subtangent in the Context of Weighted Models

Recently, reciprocal subtangent has been used as a useful tool to describe the behaviour of a density curve. Motivated by this, in the present article we extend the concept to the weighted models. Characterization results are proved for models viz. gamma, Rayleigh, equilibrium, residual lifetime, and proportional hazards. An identity under weighted distribution is also obtained when the reciprocal subtangent takes the form of a general class of distributions. Finally, an extension of reciprocal subtangent for the weighted models in the bivariate and multivariate cases are introduced and proved some useful results

Diseño de un programa de ejercicio físico e intervención en el estilo de vida, para usuarios con hipertensión sistémica primaria de la caja de compensación familiar en convenio con la entidad promotora de salud compensar

Este trabajo contempla el diseño de un programa de ejercicio físico e intervención sobre el estilo de vida para personas con hipertensión sistémica primaria (sin enfermedad subyacente). Definimos el problema en el cual basamos nuestro trabajo, concentrándonos en el manejo de la hipertensión arterial a través de modificaciones en el estilo de vida con especial énfasis en la práctica de ejercicio físico como medio de control de las cifras de tensión arterial. justificamos los beneficios para la salud que aporta este programa en la disminución del riesgo cardiovascular y la adquisición de hábitos de vida saludables.

An extended Lindley distribution

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

Space charge and dielectric response measurements to assess insulation aging of low-voltage cables used in nuclear power plants

The current design life of nuclear power plant (NPP) could potentially be extended to 80 years. During this extended plant life, all safety and operationally relevant Instrumentation & Control (I&C) systems are required to meet their designed performance requirements to ensure safe and reliable operation of the NPP, both during normal operation and subsequent to design base events. This in turn requires an adequate and documented qualification and aging management program. It is known that electrical insulation of I&C cables used in safety related circuits can degrade during their life, due to the aging effect of environmental stresses, such as temperature, radiation, vibration, etc., particularly if located in the containment area of the NPP. Thus several condition monitoring techniques are required to assess the state of the insulation. Such techniques can be used to establish a residual lifetime, based on the relationship between condition indicators and ageing stresses, hence, to support a preventive and effective maintenance program. The object of this thesis is to investigate potential electrical aging indicators (diagnostic markers) testing various I&C cable insulations subjected to an accelerated multi-stress (thermal and radiation) aging.

A Quantile-Based Probabilistic Mean Value Theorem

For non-negative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows us to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the “expected reversed proportional shortfall order”, and a new characterization of random lifetimes involving the reversed hazard rate function.

Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

Development of Lifetime Comorbidity in the World Health Organization World Mental Health Surveys

Context: Although numerous studies have examined the role of latent variables in the structure of comorbidity among mental disorders, none has examined their role in the development of comorbidity. Objective: To study the role of latent variables in the development of comorbidity among 18 lifetime DSM-IV disorders in the World Health Organization World Mental Health Surveys. Design: Nationally or regionally representative community surveys. Setting: Fourteen countries. Participants: A total of 21 229 survey respondents. Main Outcome Measures: First onset of 18 lifetime DSM-IV anxiety, mood, behavior, and substance disorders assessed retrospectively in the World Health Organization Composite International Diagnostic Interview. Results: Separate internalizing (anxiety and mood disorders) and externalizing (behavior and substance disorders) factors were found in exploratory factor analysis of lifetime disorders. Consistently significant positive time-lagged associations were found in survival analyses for virtually all temporally primary lifetime disorders predicting subsequent onset of other disorders. Within-domain (ie, internalizing or externalizing) associations were generally stronger than between-domain associations. Most time-lagged associations were explained by a model that assumed the existence of mediating latent internalizing and externalizing variables. Specific phobia and obsessive-compulsive disorder (internalizing) and hyperactivity and oppositional defiant disorders (externalizing) were the most important predictors. A small number of residual associations remained significant after controlling the latent variables. Conclusions: The good fit of the latent variable model suggests that common causal pathways account for most of the comorbidity among the disorders considered herein. These common pathways should be the focus of future research on the development of comorbidity, although several important pairwise associations that cannot be accounted for by latent variables also exist that warrant further focused study.

‘Reliability Concepts in Quantile-based Analysis of Lifetime Data

Reliability analysis is a well established branch of statistics that deals with the statistical study of different aspects of lifetimes of a system of components. As we pointed out earlier that major part of the theory and applications in connection with reliability analysis were discussed based on the measures in terms of distribution function. In the beginning chapters of the thesis, we have described some attractive features of quantile functions and the relevance of its use in reliability analysis. Motivated by the works of Parzen (1979), Freimer et al. (1988) and Gilchrist (2000), who indicated the scope of quantile functions in reliability analysis and as a follow up of the systematic study in this connection by Nair and Sankaran (2009), in the present work we tried to extend their ideas to develop necessary theoretical framework for lifetime data analysis. In Chapter 1, we have given the relevance and scope of the study and a brief outline of the work we have carried out. Chapter 2 of this thesis is devoted to the presentation of various concepts and their brief reviews, which were useful for the discussions in the subsequent chapters .In the introduction of Chapter 4, we have pointed out the role of ageing concepts in reliability analysis and in identifying life distributions .In Chapter 6, we have studied the first two L-moments of residual life and their relevance in various applications of reliability analysis. We have shown that the first L-moment of residual function is equivalent to the vitality function, which have been widely discussed in the literature .In Chapter 7, we have defined percentile residual life in reversed time (RPRL) and derived its relationship with reversed hazard rate (RHR). We have discussed the characterization problem of RPRL and demonstrated with an example that the RPRL for given does not determine the distribution uniquely

Dynamic cumulative residual Renyi’s entropy

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon’s entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi’s entropy, and study its properties.We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models

Quantile based entropy function in past lifetime

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.

A simple relation between the Leimkuhler curve and the mean residual life

In this paper, a simple relation between the Leimkuhler curve and the mean residual life is established. The result is illustrated with several models commonly used in informetrics, such as exponential, Pareto and lognormal. Finally, relationships with some other reliability concepts are also presented. (C) 2010 Elsevier Ltd. All rights reserved.