accedaCRIShttps://accedacris.ulpgc.es/jspuiThe accedaCRIS digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 22 Jul 2024 17:59:16 GMT2024-07-22T17:59:16Z5091- Behavior Of The Posterior Error Rate With Partial Prior Information In Auditinghttp://hdl.handle.net/10553/53040Title: Behavior Of The Posterior Error Rate With Partial Prior Information In Auditing
Authors: Vazquezpolo, Fj; Bastida, Ah
Abstract: Most Of the Bayesian literature on statistical techniques in auditing has focused on assessing appropriate prior density using parameters such as interest, error rate and the mean of the error amount. Frequently, prior beliefs and mathematical tractable reasons are jointly used to assess prior distributions. As a, robust Bayesian approach, we propose to replace the prior distribution with a set of prior distributions compatible with auditor's beliefs. We show how an auditor may draw the behaviour of the posterior error rate, using only partial prior information (quartiles of the prior distribution for the error rate phi and, very often, the prior distribution is assumed to be unimodal). An example is pursued in depth.
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/10553/530401995-01-01T00:00:00Z
- Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk modelhttp://hdl.handle.net/10553/42891Title: Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model
Authors: Hernandez Bastida, Agustin; Gomez Deniz, Emilio; Perez Sanchez, Jose Maria
Abstract: The distribution of the aggregate claims in one year plays an important role in Actuarial Statistics for computing, for example, insurance premiums when both the number and size of the claims must be implemented into the model. When the number of claims follows a Poisson distribution the aggregated distribution is called the compound Poisson distribution. In this article we assume that the claim size follows an exponential distribution and later we make an extensive study of this model by assuming a bidimensional prior distribution for the parameters of the Poisson and exponential distribution with marginal gamma.This study carries us to obtain expressions for net premiums, marginal and posterior distributions in terms of some well-known special functions used in statistics. Later, a Bayesian robustness study of this model is made. Bayesian robustness on bidimensional models was deeply treated in the 1990s, producing numerous results, but few applications dealing with this problem can be found in the literature.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10553/428912009-01-01T00:00:00Z
- A study of Bayesian local robustness with applications in actuarial statisticshttp://hdl.handle.net/10553/42943Title: A study of Bayesian local robustness with applications in actuarial statistics
Authors: Gómez Déniz, Emilio; Calderín Ojeda, Enrique
Abstract: Local or infinitesimal Bayesian robustness is a powerful tool to study the sensitivity of posterior magnitudes, which cannot be expressed in a simple manner. For these expressions, the global Bayesian robustness methodology does not seem adequate since the practitioner cannot avoid using inappropriate classes of prior distributions in order to make the model mathematically tractable. This situation occurs, for example, when we compute some types of premiums in actuarial statistics in order to fix the premium to be charged to an insurance policy. In this paper, analytical and simple expressions that allow us to study the sensitivity of premiums, which are usually used in automobile insurance are provided by using the local Bayesian robustness methodology. Some examples are examined by using real automobile claim insurance data.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10553/429432010-01-01T00:00:00Z
- Modelling uncertainty in insurance Bonus-Malus premium principles by using a Bayesian robustness approachhttp://hdl.handle.net/10553/42955Title: Modelling uncertainty in insurance Bonus-Malus premium principles by using a Bayesian robustness approach
Authors: Gómez Déniz, Emilio; Vázquez Polo, Francisco José
Abstract: In a standard Bayesian model, a prior distribution is elicited for the structure parameter in order to obtain an estimate of this unknown parameter. The hierarchical model is a two way Bayesian one which incorporates a hyperprior distribution for some of the hyperparameters of the prior. In this way and under the Poisson-Gamma-Gamma model, a new distribution is obtained by computing the unconditional distribution of the random variable of interest. This distribution seems to provide a better fit to the data, given a policyholders' portfolio. Furthermore, Bayes premiums are thus obtained under a bonus-malus system and solve some of the problems of surcharges which appear in these systems when they are applied in a simple manner.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10553/429552005-01-01T00:00:00Z
- A new discrete distribution: Properties and applications in medical carehttp://hdl.handle.net/10553/42890Title: A new discrete distribution: Properties and applications in medical care
Authors: Gómez Déniz, Emilio
Abstract: This paper proposes a simple and flexible count data regression model which is able to incorporate overdispersion (the variance is greater than the mean) and which can be considered a competitor to the Poisson model. As is well known, this classical model imposes the restriction that the conditional mean of each count variable must equal the conditional variance. Nevertheless, for the common case of well-dispersed counts the Poisson regression may not be appropriate, while the count regression model proposed here is potentially useful. We consider an application to model counts of medical care utilization by the elderly in the USA using a well-known data set from the National Medical Expenditure Survey (1987), where the dependent variable is the number of stays after hospital admission, and where 10 explanatory variables are analysed
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10553/428902013-01-01T00:00:00Z
- Quasi-binomial zero-inflated regression model suitable for variables with bounded supporthttp://hdl.handle.net/10553/70163Title: Quasi-binomial zero-inflated regression model suitable for variables with bounded support
Authors: Gómez Déniz, Emilio; Gallardo, D. I.; Gómez, H. W.
Abstract: In recent years, a variety of regression models, including zero-inflated and hurdle versions, have been proposed to explain the case of a dependent variable with respect to exogenous covariates. Apart from the classical Poisson, negative binomial and generalised Poisson distributions, many proposals have appeared in the statistical literature, perhaps in response to the new possibilities offered by advanced software that now enables researchers to implement numerous special functions in a relatively simple way. However, we believe that a significant research gap remains, since very little attention has been paid to the quasi-binomial distribution, which was first proposed over fifty years ago. We believe this distribution might constitute a valid alternative to existing regression models, in situations in which the variable has bounded support. Therefore, in this paper we present a zero-inflated regression model based on the quasi-binomial distribution, taking into account the moments and maximum likelihood estimators, and perform a score test to compare the zero-inflated quasi-binomial distribution with the zero-inflated binomial distribution, and the zero-inflated model with the homogeneous model (the model in which covariates are not considered). This analysis is illustrated with two data sets that are well known in the statistical literature and which contain a large number of zeros.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10553/701632020-01-01T00:00:00Z
- Bayesian heterogeneity in a meta-analysis with two studies and binary datahttp://hdl.handle.net/10553/116910Title: Bayesian heterogeneity in a meta-analysis with two studies and binary data
Authors: Martel-Escobar, María; Negrín, Miguel Ángel; Vázquez Polo, Francisco José
Abstract: The meta–analysis of two trials is valuable in many practical situations, such as studies of rare and/or orphan diseases focussed on a single intervention. In this context, additional concerns, like small sample size and/or heterogeneity in the results obtained, might make standard frequentist and Bayesian techniques inappropriate. In a meta–analysis, moreover, the presence of between–sample heterogeneity adds model uncertainty, which must be taken into consideration when drawing inferences. We suggest that the most appropriate way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta–inference is obtained as a mixture of all the meta–inferences for the cluster models, where the mixing distribution is the posterior model probability. We present a simple two–component form of Bayesian model averaging that is unaffected by characteristics such as small study size or zero–cell counts, and which is capable of incorporating uncertainties into the estimation process. Illustrative examples are given and analysed, using real sparse binomial data.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10553/1169102022-01-01T00:00:00Z
- Erratum to a new discrete distribution: properties and applications in medical care (Journal of Applied Statistics, (2013))http://hdl.handle.net/10553/42931Title: Erratum to a new discrete distribution: properties and applications in medical care (Journal of Applied Statistics, (2013))
Authors: Gómez Déniz, Emilio
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10553/429312013-01-01T00:00:00Z
- Behaviour of the posterior error rate with partial prior information in auditinghttp://hdl.handle.net/10553/48785Title: Behaviour of the posterior error rate with partial prior information in auditing
Authors: Vázquez-Polo, F. J.; Bastida, A. Hernández
Abstract: Most of the Bayesian literature on statistical techniques in auditing has focused on assessing appropriate prior density using parameters such as interest, error rate and the mean of the error amount. Frequently, prior beliefs and mathematical tractable reasons are jointly used to assess prior distributions. As a robust Bayesian approach, we propose to replace the prior distribution with a set of prior distributions compatible with auditor's beliefs. We show how an auditor may draw the behaviour of the posterior error rate, using only partial prior information (quartiles of the prior distribution for the error rate ϕ and, very often, the prior distribution is assumed to be unimodal). An example is pursued in depth. © 1995 Journals Oxford Ltd
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/10553/487851995-01-01T00:00:00Z