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Miguel A. Sordo

Bio: Miguel A. Sordo is an academic researcher from University of Cádiz. The author has contributed to research in topics: Stochastic ordering & Random variable. The author has an hindex of 15, co-authored 49 publications receiving 734 citations. Previous affiliations of Miguel A. Sordo include Polytechnic University of Turin & University of Murcia.


Papers
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TL;DR: In this article, the authors obtained ordering properties for coherent systems with possibly dependent identically distributed components based on a representation of the system reliability function as a distorted function of the common component reliability function.
Abstract: 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 distorted distributions. The main advantage of these results is that they are distribution-free with respect to the common component distribution. Moreover, they can be applied to systems with component lifetimes having a non-exchangeable joint distribution. Copyright © 2012 John Wiley & Sons, Ltd.

108 citations

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TL;DR: In this article, a new probability density function with bounded domain is presented, which is based on the generalized Lindley distribution proposed by Zakerzadeh and Dolati (2010).
Abstract: In this paper a new probability density function with bounded domain is presented. The new distribution arises from the generalized Lindley distribution proposed by Zakerzadeh and Dolati (2010). This new distribution that depends on two parameters can be considered as an alternative to the classical beta distribution. It presents the advantage of not including any special function in its formulation. After studying its most important properties, some useful results regarding insurance and inventory management applications are obtained. In particular, in insurance, we suggest a special class of distorted premium principles based on this distribution and we compare it with the well-known power dual premium principle. Since the mean of the new distribution can be normalized to give a simple parameter, this new model is appropriate to be used as a regression model when the response is bounded, being therefore an alternative to the beta regression model recently proposed in the statistical literature.

95 citations

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TL;DR: In this article, conditions for the preservation of the main reliability classes under the formation of general coherent systems were studied for both the case of systems with identically distributed components and for systems with components having different distributions.
Abstract: 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 independent and identically distributed case, that is, the components may have the (negative) aging increasing failure rate property, but the system does not have this property. In this paper, we study conditions for the preservation of the main reliability classes under the formation of general coherent systems. These results can be applied both for systems with independent or dependent components. We consider both the case of systems with identically distributed components and the case of systems with components having different distributions. Copyright © 2013 John Wiley & Sons, Ltd.

75 citations

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TL;DR: In this paper, the authors obtained ordering preservation results for generalized distorted distributions (GDD) for coherent systems with non-identically distributed components and applied them to other statistical concepts.
Abstract: 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 be used to obtain preservation results for coherent systems with non-identically distributed components. We consider both the cases of independent and dependent components. The preservation results obtained here for GDD can also be applied to other statistical concepts.

61 citations

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TL;DR: In this article, the authors consider the dispersive order and the excess wealth order to compare the variability of distorted distributions and show that the latter can be characterized in terms of a class of variability measures associated to the tail conditional distribution.
Abstract: 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 variance. Given that the tail conditional distribution is a particular distorted distribution, a natural question is whether this result can be extended to include other classes of variability measures associated to general distorted distributions. As we show in this paper, the answer is yes, by focussing on distorted distributions associated to concave distortion functions. For distorted distributions associated to more general distortions, the characterizations are stated in terms of the stronger dispersive order.

35 citations


Cited by
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TL;DR: The author does an admirable job of explaining the differences between Bayesian probability and the frequentist notion of probability, showing that, philosophically, only the Bayesian makes sense.
Abstract: (2003). Comparison Methods for Stochastic Models and Risks. Technometrics: Vol. 45, No. 4, pp. 370-371.

611 citations

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TL;DR: A new book enPDFd comparison methods for queues and other stochastic models that can be a new way to explore the knowledge and one thing to always remember in every reading time, even step by step is shown.
Abstract: Studies stochastic models of queueing, reliability, inventory, and sequencing in which random influences are considered. One stochastic mode--rl is approximated by another that is simpler in structure or about which simpler assumptions can be made. After general results on comparison properties of random variables and stochastic processes are given, the properties are illustrated by application to various queueing models and questions in experimental design, renewal and reliability theory, PERT networks and branching processes.

472 citations

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TL;DR: In this article, the authors investigate consumer choice where individuals care not only about the absolute values of consumption, but also about their status, defined as their ordinal rank in the distribution of consumption of one "positional" good.
Abstract: We investigate consumer choice where individuals care not only about the absolute values of consumption, but also about their status. This is defined as their ordinal rank in the distribution of consumption of one "positional" good. In such a situation, the consumer's problem becomes strategic as her utility will depend on the consumption choices of others. In the symmetric Nash equilibrium of the resulting game, each individual spends more on visible consumption than in the absence of a concern for status and has lower utility. Treating status endogenously allows us to analyze how exogenous changes in the distribution of income can affect individual choices. In a more affluent society, individuals spend a higher proportion of their income on the positional good, which leads to a reduction in utility at each income level. In a more equal society those with lower incomes spend more on conspicuous consumption and are worse off. We go on to analyze externality-correcting consumption taxes and subsidies.

443 citations

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TL;DR: In this paper, the effects of exogenous changes in the distribution of income were analyzed using techniques from auction theory, showing that in a richer society, almost all individuals spend more on conspicuous consumption, and individual utility is lower at each income level.
Abstract: If individuals care about their status, defined as their rank in the distribution of consumption of one "positional" good, then the consumer's problem is strategic as her utility depends on the consumption choices of others. In the symmetric Nash equilibrium, each individual spends an inefficiently high amount on the status good. Using techniques from auction theory, we analyze the effects of exogenous changes in the distribution of income. In a richer society, almost all individuals spend more on conspicuous consumption, and individual utility is lower at each income level. In a more equal society, the poor are worse off.

410 citations