Search

Measuring the impact of a publication in a fair way is a significant challenge in bibliometrics, as it must not introduce biases between fields and should enable comparison of the impact of publications from different years. In this paper, we propose a Bayesian approach to tackle this problem, motivated by empirical data demonstrating heterogeneity in citation distributions. The approach uses the a priori distribution of citations in each field to estimate the expected a posteriori distribution in that field. This distribution is then employed to normalize the citations received by a publication in that field. Our main contribution is the Bayesian Impact Score, a measure of the impact of a publication. This score is increasing and concave with the number of citations received and decreasing and convex with the age of the publication. This means that the marginal score of an additional citation decreases as the cumulative number of citations increases and increases as the time since publication of the document grows. Finally, we present an empirical application of our approach in eight subject categories using the Scopus database and a comparison with the normalized impact indicator Field Citation Ratio from the Dimensions AI database., Comment: 21 pages, 4 tables, 2 figures

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 distributions to capture this obsolescence. The corpus being examined is published in 2019 and covers 22,559 papers citing 872,442 references. Moreover, three measures to analyze the tail of the distribution are proposed: (i) cited reference survival rate, (ii) cited reference mortality rate, and (iii) cited reference percentile. These measures are interesting because the tail of the distribution collects the behavior of the citations at the time when the document starts to get obsolete in the sense that it is little cited (used). As main conclusion, the differences observed in obsolescence are so important even between disciplinary journals in the same subfield, that it would be necessary to use some measure for the tail of the citation distribution, such as those proposed in this paper, when analyzing in an appropriate way the long time impact of a journal., Comment: 33 pages, 3 figures, 9 tables

The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf) and the cumulative distribution function (cdf) of aggregated risks, modeled according to a mixture of exponential distributions. We first review the properties of the multivariate mixture of exponential distributions, to then obtain the analytical formulation for the pdf and the cdf for the aggregated distribution. We study in detail some specific families with Pareto (Sarabia et al, 2016), Gamma, Weibull and inverse Gaussian mixture of exponentials (Whitmore and Lee, 1991) claims. We also discuss briefly the computation of risk measures, formulas for the ruin probability (Albrecher et al., 2011) and the collective risk model. An extension of the basic model based on mixtures of gamma distributions is proposed, which is one of the suggested directions for future research., Comment: This is a preprint (34 pages)

In this paper we present an alternative representation of the Negative Binomial--Lindley distribution recently proposed by Zamani and Ismail (2010) which shows some advantages over the latter model. This new formulation provides a tractable model with attractive properties which makes it suitable for application not only in insurance settings but also in other fields where overdispersion is observed. Basic properties of the new distribution are studied. A recurrence for the probabilities of the new distribution and an integral equation for the probability density function of the compound version, when the claim severities are absolutely continuous, are derived. Estimation methods are discussed and a numerical application is given., Comment: 17 pages

In this paper we obtain closed expressions for the probability distribution function, when we consider aggregated risks with multivariate dependent Pareto distributions. We work with the dependent multivariate Pareto type II proposed by Arnold (1983, 2015), which is widely used in insurance and risk analysis. We begin with the individual risk model, where we obtain the probability density function (PDF), which corresponds to a second kind beta distribution. We obtain several risk measures including the VaR, TVaR and other tail measures. Then, we consider collective risk model based on dependence, where several general properties are studied. We study in detail some relevant collective models with Poisson, negative binomial and logarithmic distributions as primary distributions. In the collective Pareto-Poisson model, the PDF is a function of the Kummer confluent hypergeometric function, and in the Pareto-negative binomial is a function of the Gauss hypergeometric function. Using the data set based on one-year vehicle insurance policies taken out in 2004-2005 (Jong and Heller, 2008), we conclude that our collective dependent models outperform the classical collective models Poisson-exponential and geometric-exponential in terms of the AIC and CAIC statistics., Comment: This is a preprint (26 pages, 4 tables, 6 figures)

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of accidents and the number of deaths on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the $\mu$ and ($\mu+1$) frequency method and the maximum likelihood method; and used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed., Comment: This is a preprint (20 pages, 7 tables, 2 figures)