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http://dx.doi.org/10.5351/CKSS.2011.18.4.485

The Proportional Likelihood Ratio Order for Lindley Distribution  

Jarrahiferiz, J. (Department of Statistics, Ferdowsi University of Mashhad)
Mohtashami Borzadaran, G.R. (Department of Statistics, Ferdowsi University of Mashhad)
Rezaei Roknabadi, A.H. (Department of Statistics, Ferdowsi University of Mashhad)
Publication Information
Communications for Statistical Applications and Methods / v.18, no.4, 2011 , pp. 485-493 More about this Journal
Abstract
The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.
Keywords
Lindley distribution; likelihood ratio order; hazard rate order; mean residual life order; Lorenz order; Laplace order; proportional likelihood ratio order; increasing proportional likelihood ratio order;
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  • Reference
1 Ahmad, I. A. and Kayid, M. (2005). Characterizations of the RHR and MIT orderings and the DRHR and IMIT classes of life distribution, Probability in the Engineering and Informational Sciences, 19, 447-461.
2 Bartoszewicz, J. and Skolimowska, M. (2004). Stochastic ordering of weighted distributions, University of Wroclaw. Report No. 143, available at www.math.uni.worc.pl/mathbank/preprint.
3 Bartoszewicz, J. and Skolimowska, M. (2006). Preservation of classes of life distributions and stochastic orders under weighting, Statistics and Probability Letters, 76, 587-596.   DOI   ScienceOn
4 Belzunce, F., Ortega, E. and Ruiz, J. M. (1999). The Laplace order and ordering of residual lives, Statistics and Probability Letters, 42, 145-156.   DOI   ScienceOn
5 Elbatal, I. (2007). The Laplace order and ordering of reversed residual life, Applied Mathematical Sciences, 36, 1773-1788.
6 Gastwirth, J. L. (1971). A general definition of the Lorenz curve, Econometrica, 39, 1037-1039.   DOI   ScienceOn
7 Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application, Mathematics and Computers in Simulation, 78, 493-506.   DOI   ScienceOn
8 Ramos-Romero, H. M. and Sordo-Diaz, M. A. (2001). The Proportional likelihood ratio order and applications, Questiio, 25, 211-223.
9 Rao, C. R. (1965). On discrete distributions arising out of methods of ascertainment, Classical and Contagious Discrete Distributions, G. Patil Ed., Pergamon Press and Statistical Publishing Society, Calcutta, 320-332.
10 Ross, S. M. (1983). Stochastic Processes, Wiley, New York.
11 Sankaran, M. (1970). The discrete Poisson-Lindley distribution, Biometrics, 26, 145-149.   DOI   ScienceOn
12 Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders, Springer, New York.
13 Holgate, P. (1970). The modality of some compound Poisson distribution, Biometrika, 57, 666-667.   DOI   ScienceOn
14 Glaser, R. E. (1980). Bathtub and related failure rate characterizations, Journal of the American Statistical Association, 75, 667-672.   DOI
15 Grandell, J. (1997). Mixed Poisson Processes, Chapman and Hall, London.
16 Gupta, R. C. and Warren, R. (2001). Determination of change points of non-monotonic failure rates, Communications in Statistics-Theory and Methods, 30, 1903-1920.   DOI   ScienceOn
17 Lehmann, E. L. (1955). Ordered families of distributions, Annals of Mathematical Statistics, 26, 399-419.   DOI
18 Lindley, D. V. (1965). Introduction to Probability and Statistics from a Bayesian Viewpoint, Cambridge University Press, New York.
19 Lillo, R. E., Nanda, A. K. and Shaked, M. (2001). Some shifted stochastic order, Recent Advances in Reliability Theory, Methodology, Practice and Inference, 85-103.
20 Lindley, D. V. (1958). Fiducial distribution and Bayes theorem, Journal of the Royal Statistical Society, 20, 102-107.
21 Nanda, A. K. and Shaked, M. (2008). Partial ordering and ageing properties of order statistics when the sample size is random: A brief review, Communications in Statistics- Theory and Methods, 37, 1710-1720.   DOI   ScienceOn
22 Navarro, J. (2008). Likelihood ratio ordering of order statistics, mixtures and systems, Statistical of Planning and Inference, 138, 1242-1257.   DOI   ScienceOn
23 Neeraj, M., Nitin, G. and Ishwari, D. D. (2008). Preservation of some aging properties and stochastic order by weighted distributions, Communications in Statistics-Theory and Methods, 37, 627-644.   DOI   ScienceOn
24 Ahmed, H. and Kayid, M. (2004). Preservation properties for the Laplace transform ordering of residual lives, Statistical Papers, 45, 583-590.   DOI   ScienceOn