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

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)

Derechos Reservados Derechos reservados por el editor de la revista


Exportado de SIDERAL (2021-04-07-12:58:58)

Este artículo se encuentra en las siguientes colecciones:
Artículos



 Registro creado el 2021-04-07, última modificación el 2021-04-07


Versión publicada:
 PDF
Valore este documento:

Rate this document:
1
2
3
 
(Sin ninguna reseña)