101200 20230519145447.0 doi 10.1017/S0269964819000329 sideral 123056 ART-2021-123056 eng Badía, F.G. Universidad de Zaragoza (orcid)0000-0002-6651-3306 Log-concavity of compound distributions with applications in operational and actuarial models 2021 Access copy available to the general public Unrestricted We establish that a random sum of independent and identically distributed (i.i.d.) random quantities has a log-concave cumulative distribution function (cdf) if (i) the random number of terms in the sum has a log-concave probability mass function (pmf) and (ii) the distribution of the i.i.d. terms has a non-increasing density function (when continuous) or a non-increasing pmf (when discrete). We illustrate the usefulness of this result using a standard actuarial risk model and a replacement model.We apply this fundamental result to establish that a compound renewal process observed during a random time interval has a log-concave cdf if the observation time interval and the inter-renewal time distribution have log-concave densities, while the compounding distribution has a decreasing density or pmf. We use this second result to establish the optimality of a so-called (s, S) policy for various inventory models with a stock-out cost coefficient of dimension [$/unit], significantly generalizing the conditions for the demand and leadtime processes, in conjunction with the cost structure in these models. We also identify the implications of our results for various algorithmic approaches to compute optimal policy parameters. Copyright info:eu-repo/grantAgreement/ES/DGA/S11 info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-63978-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.561 2021 STATISTICS & PROBABILITY 63 / 125 = 0.504 2021 Q3 T2 ENGINEERING, INDUSTRIAL 43 / 50 = 0.86 2021 Q4 T3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE 69 / 87 = 0.793 2021 Q4 T3 0.357 2021 Industrial and Manufacturing Engineering 2021 Q2 Statistics, Probability and Uncertainty 2021 Q2 Management Science and Operations Research 2021 Q2 1.5 2021 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Sangüesa, C. Universidad de Zaragoza (orcid)0000-0002-7099-7665 Federgruen, A. 2007 265 Universidad de Zaragoza Dpto. Métodos Estadísticos Área Estadís. Investig. Opera. 35, 4 (2021), 201-235 Probab. eng. inf. sci. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES 0269-9648 163331 http://zaguan.unizar.es/record/101200/files/texto_completo.pdf Versión publicada 1330032 http://zaguan.unizar.es/record/101200/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:101200 articulos driver 2023-05-18-14:39:04 ARTICLE