Discrete Likelihood Ratio Order for Power Series Distribution

Orden de la razón de verosimilitud discreta para la distribución de series de potencias

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.

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.

https://doi.org/10.15446/rce.v37n1.44356

Discrete Likelihood Ratio Order for Power Series Distribution Orden de la razón de verosimilitud discreta para la distribución de series de potencias NARJES AMELI¹, JALIL JARRAHIFERIZ², GHOLAM REZA MOHTASHAMI-BORZADARAN³

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

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Abstract

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

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Resumen

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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References

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[Recibido en abril de 2013. Aceptado en diciembre de 2013]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv37n1a03,
    AUTHOR  = {Ameli, Narjes and Jarrahiferiz, Jalil and Mohtashami-Borzadaran, Gholam Reza},
    TITLE   = {{Discrete Likelihood Ratio Order for Power Series Distribution}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {1},
    pages   = {35-43}
}

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