Log-concavity of compound distributions with applications in operational and actuarial models

Badía, F.G. (Universidad de Zaragoza) ; Sangüesa, C. (Universidad de Zaragoza) ; Federgruen, A.

Resumen: 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

Idioma: Inglés

DOI: 10.1017/S0269964819000329

Año: 2021

Publicado en: PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES 35, 4 (2021), 201-235
ISSN: 0269-9648

Factor impacto JCR: 1.561 (2021)

Categ. JCR: STATISTICS & PROBABILITY rank: 63 / 125 = 0.504 (2021) - Q3 - T2
Categ. JCR: ENGINEERING, INDUSTRIAL rank: 43 / 50 = 0.86 (2021) - Q4 - T3
Categ. JCR: OPERATIONS RESEARCH & MANAGEMENT SCIENCE rank: 69 / 87 = 0.793 (2021) - Q4 - T3

Factor impacto CITESCORE: 1.5 - Engineering (Q3) - Mathematics (Q3) - Decision Sciences (Q3)

Factor impacto SCIMAGO: 0.357 - Industrial and Manufacturing Engineering (Q2) - Statistics, Probability and Uncertainty (Q2) - Management Science and Operations Research (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/S11
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-63978-P

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)