Julio Mulero

• Mathematics, Ph D
• Senior Lecturer at University of Alicante

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and provide some applications based on distorted random variables. Specifically, we consider the cases when the underlyi...

The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and $k$-ou-of-$n$ systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. I...

Considered a pair of random lifetimes whose dependence is described by a Time Transformed Exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of the joint distribution in terms of multivariate distortions, which is an alternative approach to the classical c...

In this paper we describe a general approach to optimal imperfect maintenance activities of a repairable equipment with independent components. Most of the existing works on optimal imperfect maintenance activities of a repairable equipment with independent components. In addition, it is assumed that all the components of the equipment share the sa...

In this paper we provide a new criterion for the comparison of claims, when we have conditional claims arising in stop loss contracts or contracts with franchise deductible. These stochastic comparisons are made on the basis of the Tail Value at Risk (also known as conditional tail expectation), just for a fixed level and beyond. In particular, we...

In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the exposure to to large risks. In this paper we analyze the comparison between tail values at risk from a confidence...

For a given pair of random lifetimes whose dependence is described by a time-transformed exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of the joint distribution in terms of bivariate distortions, which is an alternative approach to the classical copul...

In this paper we provide a new criterion for the comparison of claims, when we have conditional claims arising in stop loss contracts or contracts with franchise de- ductible. These stochastic comparisons are made on the basis of the Tail Value at Risk (also known as conditional tail expectation), just for a �xed level and beyond. In particular, we...

The tail value at risk at level p, with p∈(0,1), is a risk measure that captures the tail risk of losses and asset return distributions beyond the p quantile. Given two distributions, it can be used to decide which is riskier. When the tail values at risk of both distributions agree, whenever the probability level p∈(0,1), about which of them is ri...

The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and k-out-of-n systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. In t...

Most of the existing works on optimal imperfect maintenance activities of a repairable equipment with independent components consider a single model for equipment behaviour. In addition, it is assumed that all the components of the equipment share the same model and the same maintenance inter- vals and that effectiveness of maintenance is known. In...

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and provide some applications based on distorted random variables. Speci�cally, we consider the cases when the underlyin...

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and provide some applications based on distorted random variables. Specifically, we consider the cases when the underlyi...

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and provide some applications based on distorted random variables. Specifically, we consider the cases when the underlyi...

Actuarial risks and ?nancial asset returns are tipically heavy tailed. In this paper, we introduce two stochastic dominance criteria, called the right tail order and the left tail order, to compare these variables stochastically. The criteria are based on comparisons of expected utilities, for two classes of utility functions that give more weight...

In this chapter, we introduce and study some of the main multivariate stochastic orders that we can find in the literature. Again, the list is not exhaustive and the idea of this chapter is to give the reader a manageable contact with the topic of stochastic orders in the multivariate case. We provide formal definitions and some results on sufficie...

In this chapter, we introduce several concepts for univariate and multivariate distributions, which will be used in the book. We provide the definition and interpretation of some functions in several contexts, like reliability, survival analysis, risks, and economics. These functions will be used to define several stochastic orders in Chapters 2 an...

Esta obra por capítulos pretende difundir y divulgar la importancia de las matemáticas en el desarrollo de la actividad humana desde diferentes contextos y puntos de vista, señalando al mismo tiempo sus relaciones con otras disciplinas o campos de conocimiento. En particular, este libro muestra algunas conexiones de las matemáticas con la arqueolog...

The statistical literature contains many univariate and multivariate skewness mea- sures that allow two datasets to be compared, some of which are defined in terms of quantile values. In most situations, the comparison between two random vectors focuses on univariate comparisons of conditional random variables truncated in quantiles; this kind of c...

El principal objetivo de este proyecto es organizar una serie de actividades que puedan ser de interés general para todos los estudiantes de la Facultad de Ciencias. Estas actividades, ya sean cursos, seminarios o reuniones, tendrán diferentes objetivos: ayudar al estudiante a mejorar su organización y planificación; fomentar los programas de movil...

Segunda edición: Mulero, J.; Sepulcre, J.M.: LaTeX con palabras clave. ISBN: 978-84-9717-704-7, Publicaciones Universidad de Alicante, 2020 Este manual está especialmente dirigido a aquellos estudiantes, profesores o investigadores que deseen iniciarse y adquirir soltura en el manejo de LaTeX, un sistema de composición de textos que es en la actua...

Recientemente, el software estadístico R ha incluido en su repositorio un paquete de instrucciones llamado Shiny que permite la creación de aplicaciones web interactivas. En este trabajo, presentamos unos recursos docentes diseñados con Shiny que ponen al alcance de los alumnos tantos ejercicios como deseen, permitiéndoles entrenar sus capacidades...

Many criteria of ageing for random variables or vectors have been proposed in the literature over many years. For instance, a random variable is increasing in failure rate (IFR) if, and only if, it can be ordered with an exponentially distributed random variable in the univariate convex transform order proposed by van Zwet (1964). Recently, Belzunc...

In this paper, we provide a new concept of relative skewness among multivariate distributions, extending to the multivariate case a similar concept in the univariate case. In this case, a random variable \(Y\) is said to be more right skewed than a random variable \(X\) if there exists an increasing convex transformation which maps \(X\) onto \(Y\)...

An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics. The book provides a general background on this topic for students and researchers who want to use it as a tool for their research. In addition,...

Las matemáticas constituyen un lenguaje universal y la base de cualquier tipo de desarrollo científico y tecnológico. Es incuestionable que no podríamos entender el mundo sin ellas. Esta monografía, compuesta de trece capítulos escritos con un lenguaje cercano y ameno por destacados especialistas, supone un recorrido por diversos conceptos matemát...

El reconocimiento docente: innovar e investigar con criterios de calidad. ISBN: modo pertinente a las directrices del EEES. En virtud de ello, nos hemos propuesto enfocar nuestras prácticas docentes aprovechando dicha estrategia didáctica y los recursos disponibles en la Web 2.0. Ahora bien, consideramos que como paso previo a la implementación de...

a WebQuest responde a una estrategia didáctica basada en la incorporación de las TIC en el aula, cuyo sustento teórico está en las corrientes constructivistas y el aprendizaje colaborativo, siendo de este modo pertinente a las directrices del EEES. En virtud de ello, nos hemos propuesto enfocar nuestras prácticas docentes aprovechando dicha estrate...

El campus de la Universidad de Alicante reúne una serie de características que hacen de él uno de los mejores de Europa. La sensación de espacio abierto salpicado de zonas verdes ajardinadas inunda al visitante ofreciendo una perspectiva acorde a la actividad docente e investigadora realizada en el interior de los edificios que lo conforman. Más aú...

For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows 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 stoc...

La adaptación del sistema universitario español al Espacio Europeo de Educación Superior exige la inclusión de nuevas herramientas y estrategias en el proceso de enseñanza aprendizaje. En particular, implica cambios en los métodos de evaluación que evoluciona desde un sistema basado en un examen final a un nuevo sistema en el que la evaluación cont...

En este trabajo, proponemos dos nuevas generalizaciones para la comparación de distribuciones multivariantes en términos de la asimetría extendiendo al caso de vectores un concepto similar para la comparací on de variables aleatorias. En este caso, una variable aleatoria Y se dice que es m ´ as asim etrica a la derecha que otra variable X si existe...

La WebQuest responde a una estrategia didáctica basada en la incorporación de las TIC en el aula, cuyo sustento teórico está en las corrientes constructivistas y el aprendizaje colaborativo, siendo de este modo pertinente a las directrices del EEES. En virtud de ello, nos hemos propuesto enfocar nuestras prácticas docentes aprovechando dicha estrat...

Contribuir a la mejora de la calidad de la enseñanza y de los resultados de aprendizaje constituye uno de los retos en el sistema universitario actual que exige un gran esfuerzo de coordinación en las acciones de investigación e innovación a desarrollar. Para alcanzar este propósito, desde el grupo de investigación EDUTIC-ADEI (VIGROB-039) de la Un...

In this paper, we propose and study new multivariate extensions of the dispersive, right-spread, decreasing mean residual life and new better than used in expectation univariate orders. These new orders are based on the comparison of univariate marginal distributions conditional on survival data for the rest of the components. Relationships among m...

Tradicionalmente, la enseñanza de las matemáticas se suele presentar alejada de la vida cotidiana y como una disciplina tediosa y aburrida no vinculada a actividades tales como las bellas artes, la literatura, el cine o la televisión. Es por ello que consideramos oportuno tratar de analizar, desde este punto de vista, las relaciones existentes entr...

Conclusiones 1. La participación activa de los alumnos en las tareas propuestas y los resultados positivos de la encuesta de opinión nos indican que, en general, los alumnos han comprendido que necesitan herramientas informáticas para el tratamiento de datos estadísticos. 2. Los profesores involucrados valoran de forma positiva esta experiencia. Ad...

RESUMEN (ABSTRACT). La adaptación de la Universidad española al Espacio Europeo de Educación Superior (EEES) conlleva la necesidad de incorporar nuevas herramientas que faciliten el proceso de enseñanza-aprendizaje. El alumno de estadística en una titulación de la rama de Ciencias Sociales se enfrenta a una materia de matemáticas que percibe como m...

RESUMEN (ABSTRACT) Tradicionalmente, la enseñanza de las matemáticas se suele presentar alejada de la vida cotidiana y como una disciplina tediosa y aburrida no vinculada a actividades tales como las bellas artes, la literatura, el cine o la televisión. Es por ello que consideramos oportuno tratar de analizar, desde este punto de vista, las relacio...

RESUMEN (ABSTRACT). La implementación de los nuevos grados en la Universidad de Alicante ha requerido la actualización de las metodologías docentes y de evaluación, así como una adaptación de los contenidos a los nuevos planes de estudios. Frecuentemente, esta adaptación es llevada a cabo por varios profesores que necesitan coordinarse para obtener...

Introducción En el marco de implantación de los nuevos grados en la Universidad de Alicante, se ha potenciado la reestructuración y actualización de las metodologías docentes y de evaluación. La Estadística es un área de gran importancia en el estudio de las Ciencias Sociales y Jurídicas y en ocasiones presenta grandes dificultades de aprendizaje p...

Let X = (X, Y) be a pair of lifetimes whose dependence structure is described by an Archimedean survival copula, and let X t = [(X − t, Y − t) | X > t, Y > t] denotes the corresponding pair of residual lifetimes after time t ≥ 0. Multivariate aging notions, defined by means of stochastic comparisons between X and X t , with t ≥ 0, were studied in P...

Consider two random vectors X1 and X2 whose distributions are defined according to the multivariate frailty approach, and let Xk,t=[Xk−t|Xk>t], k=1,2, be the corresponding vectors of residual lifetimes at . Conditions for multivariate stochastic comparisons of random vectors described by the frailty approach have been recently presented in Misra et...

Different sufficient conditions for stochastic comparisons between random vectors have been described in the literature. In particular, conditions for the comparison of random vectors having the same copula, i.e., the same dependence structure, may be found in Müller and Scarsini (2001). Here we provide conditions for the comparison, in the usual s...

We present a recent definition of Multivariate Increasing Failure Rate (MIFR) based on the concept of multivariate dispersion. This new definition is an extension of the univariate characterization of IFR distributions under dispersive ordering of the residual lifetimes. We apply this definition to the Clayton-Oakes model. In particular, we provide...

In the literature several authors have proposed multivariate extensions of univariate aging notions such as IFR (increasing failure rate) and DMRL (decreasing mean residual life) notions. Bassan and Spizzichino [2] and Bassan, Kochar and Spizzichino [1] proposed new multivariate notions when the lifetimes of the components have exchangeable joint p...

Consider two vectors X1 and X2 of random lifetimes whose distributions are dened via the frailty approach, and let Xk;t = (Xk tj Xk > t), k = 1; 2, be the corresponding vectors of residual lifetimes at t = (t1;:::;tn);ti 2 R+;i = 1;:::;n. Here we describe sucient conditions for the stochastic comparison X1;t st X2;t for every vector t of non-negati...

RESUMEN (ABSTRACT). En el marco de implantación de los nuevos grados en la Universidad de Alicante, se ha potenciado la reestructuración y actualización de las metodologías docentes y de evaluación. La Estadística es un área de gran importancia en el estudio de las Ciencias Sociales y Jurídicas y en ocasiones presenta grandes dificultades de aprend...

RESUMEN La adaptación de la Universidad española al Espacio Europeo de Educación Superior (EEES) conlleva la necesidad de incorporar nuevas herramientas que faciliten el proceso de enseñanza-aprendizaje. El alumno de estadística en una titulación de la rama de Ciencias Sociales se enfrenta a una materia de matemáticas que percibe como muy diferente...

In this work we present a recent de?nition of Multivariate Increasing Failure Rate (MIFR) based on the concept of multivariate dispersion. This new de?nition is an extension of the univariate characterization of IFR distributions under dispersive ordering of the residual lifetimes. We apply this de?nition to the Clayton-Oakes model. In particular,...