http://dx.doi.org/10.15446/rce.v37n1.44356

¹Payam nour University of Mashhad, Department of Sciences, Mashhad, Iran. M.Sc. Email: ameli_na83@yahoo.com
²Ferdowsi University of Mashhad, School of Mathematical Sciences, Department of Statistics, Mashhad, Iran. Ph.D Student. Email: jarrahi.jalil@yahoo.com
³Ferdowsi University of Mashhad, School of Mathematical Sciences, Department of Statistics, Mashhad, Iran. Professor. Email: grmohtashami@um.ac.ir

It is well-known that some discrete distributions belong to the power series distribution (PSD) family, so it seems useful to study conditions to establish the discrete likelihood ratio order for this family. In this paper, conditions to some cases of PSD family under which the discrete likelihood ratio order we have looked at the holds. Also, we study the discrete version of the proportional likelihood ratio as an extension of the likelihood ratio order. Then we compare some members of the PSD family by discrete proportional likelihood ratio order.

Key words: Binomial distribution, Geometric distribution, Logarithmic series distribution, Negative binomial distribution, Poisson distribution, Proportional likelihood ratio order.

Es bien conocido en la literatura que algunas distribuciones discretas pertenecen a la familia de distribuciones de series de potencias (PSD, power series distributions por sus siglas en inglés). Por lo tanto, es útil estudiar algunas condiciones para establecer el orden de la razón de verosimilitud para esta familia. En este artículo, se estudian las condiciones para algunos casos de la familia PSD bajo las cuales se mantiene el orden de la razón de verosimilitud. Otros autores han introducido y estudiado el orden de la razón de verosimilitud proporcional como una extensión del orden de razón de verosimilitud para variables aleatorias continuas. Aquí, se presenta el orden de razón de verosimilitud proporcional para variables aleatorias discretas y se estudian para la familia PSD.

Palabras clave: distribución binomial, distribución binomial negativa, distribución deseries logarítmicas, distribución geométrica, distribución\linebreak Poisson, orden de la razón de verosimilitud proporcional.

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