# Alfonso Suárez LlorensUniversidad de Cádiz | UCA · Department of Statistics and Operation Research

Alfonso Suárez Llorens

PhD in Mathematics

## About

69

Publications

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Introduction

Additional affiliations

September 1996 - present

September 1996 - July 2015

## Publications

Publications (69)

In this work, a simple, fast and dry method for the fabrication of a thermochromic product with a high load of VO 2 (M1) consisting of the controlled heat treatment of pure vanadium nanoparticles in air is presented. After a complete design of experiments, it is concluded that the most direct way to attain the maximum transformation of V into VO 2...

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure...

Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of th...

The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discus...

Co-risk measures and risk contributions measures are used in portfolio risk analysis to assess and quantify the risk of contagion, given that one or more assets in the portfolio are in distress. In this paper, given two random vectors X and Y that represent two portfolios of n assets (n≥2) and exhibit some kind of positive dependence, we give suffi...

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...

In the context of robust Bayesian analysis for multiparameter distributions, we introduce a new class of priors based on stochastic orders, multivariate total positivity of order 2 (M T P 2) and weighted distributions. We provide the new definition, its interpretation and the main properties and we also study the relationship with other classical c...

The main aim of this article is to propose a conceptual support for ROC curves within the general field of inequalities by applying the theory of majorization of vectors. For our purpose, we will use the concept of sensitivity associated with a vector in Rn+ which have been recently published in literature. Based on the sensitivity concept we first...

The minimal repair replacement is a reasonable assumption in many practical systems. Under this assumption a failed component is replaced by another one whose reliability is the same as that of the component just before the failure, i.e., a used component with the same age. In this paper we study the minimal repair in coherent systems. We consider...

The literature related to system signatures is briefly discussed. In short, computing a “signature” is associated with the fact of capturing the essence of a coherent system to simplify the quantification of its reliability. In this context, a representation of the reliability function of a repairable coherent system of n components is addressed. I...

Three functional measures of the shape of univariate distributions are proposed which are consistent with respect to the convex transform order. The first two are weighted tail indices that characterize location-scale families of distributions, whilst the third is a skewness measure. Properties of the new measures are established for various classe...

We study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis , 11 (4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior unce...

We address the problem of evaluating measurements of radionuclide activity concentration from a robust Bayesian perspective. As shown in previous studies, Bayesian incorporation of available prior information on the activity levels, together with the measured values, leads in general to an improvement in the quality of radioanalytical results. Sinc...

In this paper, we study stochastic comparisons of the coherent systems obtained under different repair policies. We consider minimal repairs of the components, that is, a failed component is replaced by another component which is similar (ie, it has the same distribution) to the replaced one and with the same age. Under these assumptions, we study...

Conditional risk measures (or co-risk measures) and risk contribution measures are increasingly used in actuarial portfolio analysis to evaluate the systemic risk, which is related to the risk that the failure or loss of a component spreads to another component or even to the whole portfolio: while co-risk measures are risk-adjusted versions of mea...

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...

Comparison of residual lives and inactivity times is an important topic in reliability. In this framework, our purpose is twofold. First, we interpret a family of stochastic orders, known in the literature as transform stochastic orderings, in terms of stochastic comparisons among residual lives and inactivity times at quantiles. Second, we introdu...

A generic theoretical methodology for the calculation of the efficiency of gamma spectrometry systems is introduced in this work. The procedure is valid for any type of source and detector and can be applied to determine the full energy peak and the total efficiency of any source-detector system. The methodology is based on the idea of underlying p...

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...

We propose a new explanatory index for evaluating the binary logistic regression model based on the sensitivity of the estimated model. We previously formalized the idea of sensitivity and established the principles a statistic should comply with to be considered a sensitivity index. We apply the results to a practical example and compare the resul...

In this paper, we derive a measure of discrepancy based on the Gini’s mean difference to test the null hypothesis that two random variables, which are ordered in a variability-type stochastic order, are equally dispersive versus the alternative that one strictly dominates the other. We describe the test, evaluate its performance under a variety of...

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 the context of robust Bayesian analysis, we introduce a new class of prior distributions based on stochastic orders and distortion functions. We provide the new definition, its interpretation and the main properties and we also study the relationship with other classical classes of prior beliefs. We also consider Kolmogorov and Kantorovich metri...

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 \(Y\)...

We present a generalized signature in repairable coherent systems resembling Samaniego's notion for statistically independent and identically distributed lifetimes. The repairable systems are made of different components which can individually fail, and be minimally repaired up to a fixed number of times. Failures occur according to Poisson process...

In the paper, we address Bayesian sensitivity issues when integrating experts' judgments with available historical data in a case study about strategies for the preventive maintenance of low-pressure cast iron pipelines in an urban gas distribution network. We are interested in replacement priorities, as determined by the failure rates of pipelines...

El satélite artificial GAIA (http://sci.esa.int/gaia/) es una de las misiones
espaciales más ambiciosas que desarrolla la Agencia Espacial Europea en estos
momentos. El gran reto científico y tecnológico que se pretende conseguir con
esta misión es la de registrar diferentes magnitudes físicas, con especial
interés en la precisión de la distancia,...

The preservation of stochastic orders under the formation of coherent systems is a relevant topic in the reliability theory. Several properties have been obtained under the assumption of identically distributed components. In this paper we obtain ordering preservation results for generalized distorted distributions (GDD) which, in particular, can b...

The situation of the current economic crisis and its impact on the labour market, with a significant increase in unemployment levels in some of the member countries of the EU, reinforces the role of employment promotion policies as an element of social cohesion. This is an important moment to enhance the association between public and private actio...

Given a portfolio of risks, we study the marginal behavior of the -th risk under an adverse event, such as an unusually large loss in the portfolio or, in the case of a portfolio with a positive dependence structure, to an unusually large loss for another risk. By considering some particular conditional risk distributions, we formalize, in several...

Alzheimer's disease (AD) is the most common cause of dementia in the adult population. Tools capable of detecting predementia and established diagnoses of dementia are very important for assessing these patients. The Repeatable Battery for the Assessment of Neuropsychological Status (RBANS) is a brief neuropsychological battery that has been succes...

In this paper, we introduce a new variability order that can be interpreted in terms of tail-heaviness which we will call the tail dispersive order. We provide the new definition, its interpretation and properties and the main characterization. We also study the relationship with other classical variability orders. Finally, we study the tail disper...

The preservation of reliability aging classes under the formation of coherent systems is a relevant topic in reliability theory. Thus, it is well known that the new better than used class is preserved under the formation of coherent systems with independent components. However, surprisingly, the increasing failure rate class is not preserved in the...

Two basic ideas that give rise to global dependence stochastic orders were introduced and studied in Shaked et al. (Methodology and Computing in Applied Probability 14:617–648, 2012). Here these are reviewed, and two new ideas that give rise to new global dependence orders are then brought out and discussed. Two particular global dependence orders...

In this paper, we obtain ordering properties for coherent systems with possibly dependent identically distributed components. These results are based on a representation of the system reliability function as a distorted function of the common component reliability function. So, the results included in this paper can also be applied to general disto...

In actuarial theory, the Lp-metric is used to evaluate how well a probability distribution approximates another one. In the context of the distorted expectation hypothesis, the actuary replaces the original probability distribution by a distorted probability, so it makes sense to interpret the Lp-metric between them as a characteristic of the under...

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...

Let X and Y be two randomvectors sharing the same dependence structure, that is, with a common copula. As many authors have pointed out, results of the following form are of interest: under which conditions, the stochastic comparison of the marginals of and is a sufficient condition for the comparison of the expected values for some transformations...

Two basic ideas, that give rise to global dependence stochastic orders, are introduced and studied. The similarities and differences
between the resulting global dependence orders, and the known common positive dependence orders, are discussed. Some desirable
properties that global dependence orders may expected to satisfy are listed and checked. T...

In this paper, we consider the dispersive order and the excess wealth order to compare the variability of distorted distributions. We know from Sordo (2009a) that the excess wealth order can be characterized in terms of a class of variability measures associated to the tail conditional distribution which includes, as a particular measure, the tail...

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also ordered in the increasing convex order. This result is ex...

Li and Shaked (2007) introduced the family of generalized total time on test transform (TTT) stochastic orders, which is parameterized by a real function h that can be used to capture the preferences of a decision maker. It is natural to look for properties of these orders when there is an uncertainty in determining the appropriate function h. In t...

Li and Shaked (2007) introduced the family of generalized total time on test transform (TTT) stochastic orders, which is parameterized by a real function h that can be used to capture the preferences of a decision maker. It is natural to look for properties of these orders when there is an uncertainty in determining the appropriate function h . In...

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...

Partiendo de una muestra de 765 pequeñas y medianas empresas, este artículo presenta un estudio exploratorio de la medida en la que la propiedad familiar incide sobre la orientación estratégica de este tipo de organizaciones. A través de un análisis clúster, se identificaron conglomerados de empresas dentro de la muestra, que se asocian con diferen...

In bayesian inference, the Bayes estimator is the alternative with the minimum expected loss. In most cases, the loss function shows the distance between the alternative and the parameter. Therefore, any distance can lead to a loss function. Among the best known distance functions is L
p
one, where the choice of value p may be difficult and arbitra...

In this paper we present a definition of multivariate increasing failure rate based on the concept of multivariate dispersion. This new definition is an extension of the univariate characterization of increasing failure rate distributions under dispersive ordering of the residual lives. We study this definition in the Clayton–Oakes model and the fa...

Researches in Bayesian sensitivity analysis and robustness have mainly dealt with the computation of the range of some quantities of interest when the prior distribution varies in some class. Recently, researchers’ attention turned to the loss function, mostly to the changes in posterior expected loss and optimal actions. In particular, the search...

Este estudio analiza las actitudes e itnenciones emprendedoras de los estudiantes de las universidades públicas de Andalucía. Parte del supuesto de que las intenciones de las personas subyacen como factor decisivo en los procesos de creación de empresas y desarrollo empresarial. Se analizan un conjunto de factores, que influyen en la intención empr...

Se analiza la situación de las actitudes e intenciones emprendedoras de los estudiantes de las universidades públicas de Andalucía. Una muestra amplia de mas de 3000 estudiantes de 9 universidades.
Se analizan las intenciones, viabilidad, autoconfianza, deseabilidad, imagen del empresario, los familiares empresarios y el papel de la universidad.
E...

We study the relationship between the multivariate dispersive orders based on the standard construction. In particular those given by Shaked and Shanthikumar [1998. Two variability orders. Probab. Eng. Inform. Sci. 12, 1-23] and Fernández-Ponce and Suárez-Llorens [2003. A multivariate dispersion ordering based on quantiles more widely separated. J....

Within the context of a general bivariate distribution an intuitive method is presented in order to study the dependence structure of the two distributions. A set of points—level curve—which accumulate the same probability for a fixed quadrant is considered. This procedure provides four level curves which can be considered as the boundary of a gene...

Bayesian decision problems require subjective elicitation of the inputs: beliefs and preferences. Sometimes, elicitation methods may not represent perfectly the judgements of the decision maker. Several foundations propose to overlay this problem using robust approaches. In these models, beliefs are modelled by a class of probability distributions...

We study the concept of multivariate dispersion order, defined as the
existence of an expansion function that maps a random vector to another
one, for multivariate distributions with the same dependence structure. As
a particular case, we can order the multivariate t-distribution
family in dispersion sense. Finally, we use these results in the...

A multivariate dispersion ordering based on quantiles more widely separated is defined. This new multivariate dispersion ordering is a generalization of the classic univariate version. If we vary the ordering of the components in the multivariate random variable then the comparison could not be possible. We provide a characterization using a multiv...

In this article we study the comparison of experiments in system reliability theory when the component lifetimes are independent and identically distributed random variables that have a common two-parameter exponential distribution with a location parameter θ. For this purpose, we define a new stochastic order, which we call the convolution order,...

Bayes decision problems require subjective elicitation of the inputs: beliefs and preferences. Sometimes, elicitation methods may not perfectly represent the Decision Maker's judgements. Several foundations propose to overlay this problem using robust approaches. In these models, beliefs are modelled by a class of probability distributions and pref...

In this article, we introduce a new dispersion order weaker
than the classic dispersion order discussed by Lewis and Thompson
(1981). We study the equivalence of this order with the
majorization order under the assumption of unimodality. Finally,
we use this equivalence to characterize the IFR aging notion
for unimodal distributions by means o...

For a one-dimensional probability distribution, the classical concept of central region as a real interquantile interval arises in all applied sciences. We can find applications, for instance, with dispersion, skewness and detection of outliers. All authors agree with the main problem in a multivariate generalization: there does not exist a natural...

In a recent work, Ollero and Ramos (1995) using the descriptionof the Pólya distribution as a generalised binomial distribution, compared the cumulative distribution functions (cdf) of the Pólya distirbution P(N,p,n,c) when c<0 and the Binomial distribution B(p,n). This comparison is done everywhere but in an interval with amplitude equal to 1.

MacArthur broken stick model of relative abundace of species, has been applied to almost every posible level of organization. When comparing several fits to the broken stick distribution, it becomes necessary to make some evaluation of the goodness-of-fit of the tests. We present a result that can be useful to make this evaluation.

Este trabajo plantea un análisis empírico de las diferencias de eficiencia entre las empresas familiares y no familiares, medida a través de tres indicadores subrogados (rentabilidad financiera, rentabilidad económica y margen de explotación). El estudio empírico, desarrollado sobre una muestra de 765 empresas andaluzas, no permite contrastar ningu...

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,...

## Projects

Projects (2)