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Publications (66)
In this brief note, we provide, as far as we know, a simple way to demonstrate that when we multiply $k\times n$ matrix with $n\times k$ one, for $k>n$, we always obtain singular $k\times k$ matrix as a result. Some additional results are also provided.
There are different citation habits in the research fields that influence the obsolescence of the research literature. We analyze the distinctive obsolescence of research literature in disciplinary journals in eight scientific subfields based on cited references distribution, as a synchronous approach. We use both negative binomial (NB) and Poisson...
In this paper, reference analysis, the tool provided by Berger et al. (2009), is used to obtain reference Bayesian premiums, which can be helpful when the practitioner has insufficient information to elicit a prior distribution. The Bayesian premiums thus obtained are based exclusively on prior distributions built from the model generated and from...
There are different citation habits in the research fields that influence the obsolescence of the research literature. We analyze the distinctive obsolescence of research literature in disciplinary journals in eight scientific subfields based on cited references distribution, as a synchronous approach. We use both Negative Binomial (NB) and Poisson...
Many factors are involved in tourist decision expenses. Such circumstances may give rise to some asymmetry in the distribution of tourism expenditure. We propose in this paper a reparameterization of the three-parameter log-skew normal distribution for modelling the expenditure at the country of origin, at destination, and total expenditure in a to...
In this paper, a new family of continuous random variables with non-necessarily symmetric densities is introduced. Its density function can incorporate unimodality and bimodality features. Special attention is paid to the normal distribution which is included as a particular case. Its density function is given in closed-form which allows to easily...
In this paper, the three-parameter skew lognormal distribution is proposed to model actuarial data concerning losses. This distribution yields a satisfactory fit to empirical data in the whole range of the empirical distribution as compared to other distributions used in the actuarial statistics literature. To the best of our knowledge, this distri...
A new compound non-symmetric distribution for modeling arbitrary fading-shadowing wireless channels is introduced and studied here. This distribution has some advantages in front of other well-known non-symmetric fading distributions such as the Rayleigh–lognormal distribution and the K distribution especially in the tails. We give closed-form expr...
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, perh...
Empirically, the length of stay by tourists at their destination usually presents bimodality, overdispersion and non-zero observations, and classical distributions do not seem to fit this type of data very appropriately. In this paper, we introduce two distributions which accommodate bimodality. One is a flexible discrete distribution which can be...
We propose an alternative distribution for modelling fading-shadowing wireless channels. This distribution presents certain advantages over the Rayleigh-lognormal distribution and the K distribution and has proved useful in the setting described. We obtain closed-form expressions for the average channel capacity and for the average bit error rate o...
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...
The aim of this article is to obtain a statistical distribution that describes the aggregate expenditure of tourists related to their length of stay at a given location. This distribution enables us to estimate two parameters simultaneously; one controls the length of stay and the other, the expense incurred. We propose two distribution models, for...
In this paper , a new discrete two–parameter distribution α ∈ ℜ − {0} and 0 < θ < 1, the Geometric ArcTan (GAT) distribution is introduced. The geometric distribution is a limiting case of this model when α tends to zero. Similarly to the the latter distribution, this probabilistic family is unimodal but the mode can be located at zero or in other...
The barely known continuous reciprocal inverse Gaussian distribution is used in this paper to introduce the Poisson-reciprocal inverse Gaussian discrete distribution. Several of its most relevant statistical properties are examined, some of them directly inherited from the reciprocal of the inverse Gaussian distribution. Furthermore, a mixed Poisso...
The main purpose of this paper is to present an asymmetric logit probability model to estimate and
predict the daily probabilities of delay in aircraft arrivals. The proposed model takes into account statistical
regularity, noting that more arrivals are on time than delayed, thus reflecting an asymmetric
pattern of behaviour. The data analysed were...
A new one-parameter family of discrete distributions is presented. It has some advantages against the Poisson distribution as a suitable model for modelling data with a high frequencies of zeros and showing over-dispersion (variance larger than the mean). The distribution is obtained from a simple modification of the Borel-Tanner distribution, whic...
Following the recent work of Gómez-Déniz and Pérez-Rodríguez (2014), this paper extends the results obtained there to the normal-exponential distribution with dependence. Accordingly, the main aim of the present paper is to enhance stochastic production frontier and stochastic cost frontier modelling by proposing a bivariate distribution for depend...
This work proposes a one–parameter distribution with a formulation that involves the double factorial. The new distribution is intended to be competitive with the Poisson, geometric and negative binomial distributions and, like these, belongs to the natural exponential family of distributions (EFD) and to power series distributions. The new distrib...
This paper presents a competent and useful way to elaborate random exams by using Mathematica and LATEX. With these two tools, the authors suggest how to generate, in an easy way, different PDF documents containing different models of exams. The main idea is to provide a support to professors who have to manage groups of large number of students th...
p>This paper extends the conditional duration model proposed by De Luca and Zuccolotto (2003), proposing an infinite mixture of distributions based on non–exponentials which accounts for the unobserved market heterogeneity of traders. The model we propose takes into account the fact that reaction times follow a gamma distribution and that the inten...
In this paper a mixed Poisson regression model for count data is introduced. This model is derived by mixing the Poisson distribution with the one-parameter continuous exponential-inverse Gaussian distribution. The obtained probability mass function is over-dispersed and unimodal with modal value located at zero. Estimation is performed by maximum...
This paper proposes bivariate version of the univariate discrete generalized geometric distribution considered by Gómez–Déniz (20106.
Gómez–Déniz, E. (2010). Another generalization of the geometric distribution. Test, 19, 399–415.View all references). The proposed bivariate distribution can have positive or negative correlation coefficient which ca...
We propose a modification of the bonus–malus system of tarification that is commonly applied in automobile insurance. Under the standard system, the premium assigned to each policyholder is based only on the number of claims made. Therefore, a policyholder who has had an accident producing a relatively small amount of loss is penalised to the same...
A new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating...
Generalized linear models (GLMs) that use a regression procedure to fit relationships between predictor and target variables are widely used in risk insurance data. It is crucial to detect the risk factors that significatively affect the number of claims, as this will eventually allow the insurer to fix premiums more precisely. We pay attention to...
A generalization of the geometric distribution is obtained after mixing the Poisson distribution with the generalized exponential distribution in Marshall and Olkin in 1997. The discrete distribution is defined through a new special function also introduced in this manuscript. Unimodality is highlighted among the properties of this two-parameter di...
In this paper, we have developed a Poisson-mixed inverse Gaussian (PMIG) distribution. The mixed inverse Gaussian distribution is a mixture of the inverse Gaussian distribution and its length biased counter part. A PMIG regression model is developed and the maximum likelihood estimation of the parameters is studied. A data set dealing with the numb...
Bivariate distributions, specified in terms of their conditional distributions, provide a powerful tool to obtain flexible distributions. These distributions play an important role in specifying the conjugate prior in certain multi-parameter Bayesian settings. In this paper, the conditional specification technique is applied to look for more flexib...
A new discrete distribution depending on two parameters
$\alpha >-1$
and
$\sigma >0$
is obtained by discretizing the generalized normal distribution proposed in García et al. (Comput Stat and Data Anal 54:2021–2034, 2010), which was derived from the normal distribution by using the Marshall and Olkin (Biometrika 84(3):641–652, 1997) scheme. The...
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 n...
In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occurs in practical situations. The distribution proposed is derived from the lognormal distribution, by using the Marshall and Olkin procedure. Some basic properties of this new distribution are obtained and we present situations where this new...
A new class of heavy–tailed distribution functions, containing the lognormal distribution as a particular case, is introduced. The class thus obtained depends on a set of three parameters, incorporating an additional distribution to the classical lognormal one. This new class of heavy-tailed distribution is presented as an alternative to other usef...
An extension of the discrete Lindley distribution is obtained by discretizing the continuous failure rate model in the generalized continuous distribution in Zakerzadeh and Dolati [Zakerzadeh, Y., & Dolati, A. (2009). Generalized Lindley distribution. Journal of Mathematical Extension, 3(2), 13–25]. The result is a generalization of the geometric d...
The signal received in a mobile radio environment exhibits rapid signal level fluctuations which are generally Rayleigh-distributed. These result from interference by multiple scattered radio paths between the base station and the mobile receptor. Fading-shadowing effects in wireless channels are usually modelled by means of the Rayleigh–Lognormal...
In this paper the collective risk model with Poisson–Lindley and exponential distributions as the primary and secondary distributions, respectively, is developed in a detailed way. It is applied to determine the Bayes premium used in actuarial science and also to compute the regulatory capital in the analysis of operational risk. The results are il...
In this article we propose multivariate versions of the beta mixture of Poisson distribution considered by Gurland (19589.
Gurland , J. ( 1958 ). A generalized class of contagious distributions . Biometrics 14 : 229 – 249 . [CrossRef], [Web of Science ®]View all references), Katti (196616.
Katti , S. K. ( 1966 ). Interrelations among generalized di...
This paper focuses on the study of the Collective and Bayes Premiums, under the Variance Premium Principle, in the classic Collective Risk Poisson-Exponential Model. A bivariate prior distribution is considered for both the parameter of the distribution of the number of claims and that of the distribution of the claim amount, assuming independence...
Modelling the claim frequency is one of the most important issues in Risk Theory. In this chapter, two new probability distribution are introduced, a two-parameter probability density function, including a wide variety of curve shapes, and a two-parameter probability mass function. The latter, obtained by mixing the classical Poisson distribution w...
Let L0 consider an initial Lorenz curve. In this paper we propose a general methodology for obtaining new classes of parametric Lorenz or Leimkuhler curves that contain the original curve as limiting or special case. The new classes introduce additional parameters in the original family, providing more flexibility for the new families. The new clas...
A new generalization of the geometric distribution with parameters α>0 and 0<θ<1 is obtained in this paper. This can be done either by using the Marshall and Olkin (Biometrika 84(3), 641–652, 1997) scheme and adding a parameter to the geometric distribution or by starting with the generalized exponential distribution
in Marshall and Olkin (Biometri...
A new class of distribution functions with not-necessarily symmetric densities, which contains the normal one as a particular case, is introduced. The class thus obtained depends on a set of three parameters, with an additional one to the classical normal distribution being inserted. This new class of skewed distributions is presented as an alterna...
In Bayesian analysis it is usual to assume that the risk profiles [Theta]1 and [Theta]2 associated with the random variables "number of claims" and "amount of a single claim", respectively, are independent. A few studies have addressed a model of this nature assuming some degree of dependence between the two random variables (and most of these stud...
In credibility theory, the premium charged to a policyholder is computed on the basis of
his/her own past claims and the accumulated past claims of the corresponding portfolio of
policyholders. In order to obtain an appropriate formula for this, various methodologies
have been proposed in actuarial literature, most of them in the field of Bayesian...
In this article, we consider Bayesian statistical models in which prior distribution of the risk parameter is to be specified in a hierarchical fashion. The model obtained is shown to be over-dispersed and competitive with other models in the literature for fitting automobile claim frequency data. We obtain analytical forms of the distribution, whi...
In this paper an alternative to the usual credibility premium that arises for weighted balanced loss function is considered. This is a generalized loss function which includes as a particular case the weighted quadratic loss function traditionally used in actuarial science. From this function credibility premiums under appropriate likelihood and pr...
In this paper we propose a new compound negative binomial distribution by mixing the p negative binomial parameter with an inverse Gaussian distribution and where we consider the reparameterization p=exp(-[lambda]). This new formulation provides a tractable model with attractive properties which make it suitable for application not only in the insu...
The distribution of the aggregate claim size is the considerable importance in insurance theory since, for example, it is needed as an input in premium calculation principles and reserve calculation which plays an important paper in ruin theory. In this paper a Bayesian study for the collective risk model by incorporating a prior distribution for b...
This article develops a Bayesian analysis of the Compound Collective Model utilizing the Net Premium Principle, considering single-period models. With respect to likelihoods, we used a Poisson distribution for the number of claims and an Exponential distribution for the severity of the accident/event. Gamma distributions were used for the prior dis...
Computing premiums in a Bayesian context requires the use of a prior distribution that the unknown risk parameter follows in the heterogeneous portfolio. Following the methodology that an actuary only has vague information about this parameter and therefore is unable to specify a simple prior, we choose a class Gamma of priors and compute posterior...
In this article we measure the local or infinitesimal sensitivity of a kind of Bayes estimates which appear in bonus–malus systems. Bonus–malus premiums can be viewed as a functional depending on the prior distribution. To measure when small changes in the prior cause large changes in the premium we compute the norm of the Fréchet derivative and pr...
In this paper we consider statistical problems arising from applications concerning insurance-premium calculation. We describe
an integrated set of Bayesian tools for modelling bonus-malus systems (BMS) for insurance premiums. This paper describes a
bonus-malus system (BMS) applicable to insurance claims procedures, constructed using a hierarchical...
In this article, a new methodology for obtaining a premium based on a broad class of conjugate prior distributions, assuming lognormal claims, is presented. The new class of prior distributions arise in a natural way, using the conditional specification technique introduced by Arnold, Castillo, and Sarabia (1998, 1999). The new family of prior dist...
When Bayesian models are implemented for a Bonus–Malus System (BMS), a parametric structure, π0 (λ), is normally included in the insurer's portfolio. Following Bayesian sensitivity analysis, it is possible to model the structure function by specifying a class Γ of priors instead of a single prior. This paper examines the ranges of the relativities...
The use of classical bonus–malus systems entails very high maluses and other problems which, during recent years, have been criticised by actuaries. To avoid these problems, new bonus–malus models have been developed. For instance, it is well known that the use of an exponential loss function reduces the differences between overcharges and undercha...
El propósito principal de los sistemas de tarificación Bonus-Malus es que los asegurados paguen una prima justa, esto es la prima que corresponda a su propia experiencia de reclamación. Sin embargo, la mayoría de estos sistemas penalizan injustamente a determinados asegurados, haciéndoles pagar más de lo que realmente les corresponde. En este traba...
The paper presents a Bayesian sensitivity analysis for the credibility theory related to the net premium principle. Thus, the mixture model in prior distribution is used for the separation of subpopulations. This construction is adapted to the usual robust Bayesian results and these are exploited to obtain lower and upper bounds for the premium. Tw...
This paper considers the collective risk model for the insurance claims process. We will adopt a Bayesian point of view, where uncertainty concerning the specification of the prior distribution is a common question. The robust Bayesian approach uses a class of prior distributions which model uncertainty about the prior, instead of a single distribu...
In this paper the Esscher premium calculation principle is applied to the non-compound collective model in a robust Bayesian context. We consider that uncertainty with regard to the prior distribution can be represented by the assumption that the unknown prior distribution belongs to a class of distributions Gamma and examine the ranges of the Baye...
Premium computation in a Bayesian context requires the use of a prior distribution (structure function) that the risk parameter follows in the heterogeneous portfolio. This paper contributes to the analysis of credibility theory by identifying the unique relation-ship between the prior distribution and credibility formula. The latter corresponds to...
