Published

2014-01-01

Discrete Likelihood Ratio Order for Power Series Distribution

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

DOI:

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

Keywords:

Binomial distribution, Geometric distribution, Logarithmic series distribution, Negative binomial distribution, Poisson distribution, Proportional likelihood ratio order. (en)
distribución binomial, distribución binomial negativa, distribución de series logarítmicas, distribución geométrica, distribución Poisson, orden de la razón de verosimilitud proporcional (es)

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Authors

  • Narjes Ameli Payam nour University of Mashhad
  • Jalil Jarrahiferiz Ferdowsi University of Mashhad
  • Gholam Reza Mohtashami-Borzadaran Ferdowsi University of Mashhad

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

Abstract

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.

Resumen

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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References

1. Bartoszewicz, J. (2009), 'On a represervation of weighted distributions', Statistics and Probability Letters 79, 1690-1694.

2. Belzunce, F., Ruiz, J. M. & Ruiz, C. (2002), 'On preservation of some shifted and proportional orders by systems', Statistics and Probability Letters 60, 141-154.

3. Blazej, P. (2008), 'Reservation of classes of life distributions under weighting with a general weight function', Statistics and Probability Letters 78, 3056-3061.

4. Hu, T., Nanda, A. K., Xie, H. & Zhu, Z. (2003), 'Properties of some stochastic orders: A unified study', Naval Research Logistic 51, 193-216.

5. Lillo, R. E., Nanda, A. K. & Shaked, M. (2001), 'Preservation of some likelihood ratio stochastic orders by order statistics', Statistics and Probability Letters 51, 111-119.

6. Misra, N., Gupta, N. & Dhariyal, I. (2008), 'Preservation of some aging properties and stochastic orders by weighted distributions', Communications in Ststistics-Theory and Methods 37, 627-644.

7. Navarro, J. (2008), 'Likelihood ratio ordering of order statistics, mixture and systems', Statistical of Planning and Inference 138, 1242-1257.

8. Noack, A. (1950), 'A class of random variables with discrete distributions', Annals of Mathematical Statistics 21, 127-132.

9. Patil, G. P. (1961), Contributions to estimation in a class of discrete distributions, Ph.D thesis, University of Michigan.

10. Patil, G. P. (1962), 'Certain properties of the generalized power series distributions', Annals of the Statistical Mathematics 14, 179-182.

11. Ramos-Romero, H. M. & Sordo-Diaz, M. A. (2001), 'The proportional likelihood ratio order and applications', Questiio 25, 211-223.

12. Shaked, M. & Shanthikumar, J. G. (2007), Stochastic Orders, 1 edn, Academic Press, New York.

13. Shanthikumar, J. G. & Yao, D. D. (1986), 'The preservation of likelihood ratio ordering under convolutions', Stochastic Processes and their Applications 23, 259-267.

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

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}
}

References

Bartoszewicz, J. (2009), ‘On a represervation of weighted distributions’, Statistics and Probability Letters 79, 1690–1694.

Belzunce, F., Ruiz, J. M. & Ruiz, C. (2002), ‘On preservation of some shifted and proportional orders by systems’, Statistics and Probability Letters 60, 141–154.

Blazej, P. (2008), ‘Reservation of classes of life distributions under weighting with a general weight function’, Statistics and Probability Letters 78, 3056–3061.

Hu, T., Nanda, A. K., Xie, H. & Zhu, Z. (2003), ‘Properties of some stochastic orders: A unified study’, Naval Research Logistic 51, 193–216.

Lillo, R. E., Nanda, A. K. & Shaked, M. (2001), ‘Preservation of some likelihood ratio stochastic orders by order statistics’, Statistics and Probability Letters 51, 111–119.

Misra, N., Gupta, N. & Dhariyal, I. (2008), ‘Preservation of some aging properties and stochastic orders by weighted distributions’, Communications in Ststistics-Theory and Methods 37, 627–644.

Navarro, J. (2008), ‘Likelihood ratio ordering of order statistics, mixture and systems’, Statistical of Planning and Inference 138, 1242–1257.

Noack, A. (1950), ‘A class of random variables with discrete distributions’, Annals of Mathematical Statistics 21, 127–132.

Patil, G. P. (1961), Contributions to estimation in a class of discrete distributions, Ph.D thesis, University of Michigan.

Patil, G. P. (1962), ‘Certain properties of the generalized power series distributions’, Annals of the Statistical Mathematics 14, 179–182.

Ramos-Romero, H. M. & Sordo-Diaz, M. A. (2001), ‘The proportional likelihood ratio order and applications’, Questiio 25, 211–223.

Shaked, M. & Shanthikumar, J. G. (2007), Stochastic Orders, 1 edn, Academic Press, New York.

Shanthikumar, J. G. & Yao, D. D. (1986), ‘The preservation of likelihood ratio ordering under convolutions’, Stochastic Processes and their Applications 23, 259–267.

How to Cite

APA

Ameli, N., Jarrahiferiz, J. and Mohtashami-Borzadaran, G. R. (2014). Discrete Likelihood Ratio Order for Power Series Distribution. Revista Colombiana de Estadística, 37(1), 35–43. https://doi.org/10.15446/rce.v37n1.44356

ACM

[1]
Ameli, N., Jarrahiferiz, J. and Mohtashami-Borzadaran, G.R. 2014. Discrete Likelihood Ratio Order for Power Series Distribution. Revista Colombiana de Estadística. 37, 1 (Jan. 2014), 35–43. DOI:https://doi.org/10.15446/rce.v37n1.44356.

ACS

(1)
Ameli, N.; Jarrahiferiz, J.; Mohtashami-Borzadaran, G. R. Discrete Likelihood Ratio Order for Power Series Distribution. Rev. colomb. estad. 2014, 37, 35-43.

ABNT

AMELI, N.; JARRAHIFERIZ, J.; MOHTASHAMI-BORZADARAN, G. R. Discrete Likelihood Ratio Order for Power Series Distribution. Revista Colombiana de Estadística, [S. l.], v. 37, n. 1, p. 35–43, 2014. DOI: 10.15446/rce.v37n1.44356. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/44356. Acesso em: 12 oct. 2024.

Chicago

Ameli, Narjes, Jalil Jarrahiferiz, and Gholam Reza Mohtashami-Borzadaran. 2014. “Discrete Likelihood Ratio Order for Power Series Distribution”. Revista Colombiana De Estadística 37 (1):35-43. https://doi.org/10.15446/rce.v37n1.44356.

Harvard

Ameli, N., Jarrahiferiz, J. and Mohtashami-Borzadaran, G. R. (2014) “Discrete Likelihood Ratio Order for Power Series Distribution”, Revista Colombiana de Estadística, 37(1), pp. 35–43. doi: 10.15446/rce.v37n1.44356.

IEEE

[1]
N. Ameli, J. Jarrahiferiz, and G. R. Mohtashami-Borzadaran, “Discrete Likelihood Ratio Order for Power Series Distribution”, Rev. colomb. estad., vol. 37, no. 1, pp. 35–43, Jan. 2014.

MLA

Ameli, N., J. Jarrahiferiz, and G. R. Mohtashami-Borzadaran. “Discrete Likelihood Ratio Order for Power Series Distribution”. Revista Colombiana de Estadística, vol. 37, no. 1, Jan. 2014, pp. 35-43, doi:10.15446/rce.v37n1.44356.

Turabian

Ameli, Narjes, Jalil Jarrahiferiz, and Gholam Reza Mohtashami-Borzadaran. “Discrete Likelihood Ratio Order for Power Series Distribution”. Revista Colombiana de Estadística 37, no. 1 (January 1, 2014): 35–43. Accessed October 12, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/44356.

Vancouver

1.
Ameli N, Jarrahiferiz J, Mohtashami-Borzadaran GR. Discrete Likelihood Ratio Order for Power Series Distribution. Rev. colomb. estad. [Internet]. 2014 Jan. 1 [cited 2024 Oct. 12];37(1):35-43. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/44356

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