Advanced SearchSearch Tips
The Proportional Likelihood Ratio Order for Lindley Distribution
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
The Proportional Likelihood Ratio Order for Lindley Distribution
Jarrahiferiz, J.; Mohtashami Borzadaran, G.R.; Rezaei Roknabadi, A.H.;
  PDF(new window)
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.
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;
 Cited by
Higher order moments of order statistics from the Lindley distribution and associated inference, Journal of Statistical Computation and Simulation, 2016, 86, 17, 3432  crossref(new windwow)
Ahmed, H. and Kayid, M. (2004). Preservation properties for the Laplace transform ordering of residual lives, Statistical Papers, 45, 583-590. crossref(new window)

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.

Bartoszewicz, J. and Skolimowska, M. (2004). Stochastic ordering of weighted distributions, University of Wroclaw. Report No. 143, available at

Bartoszewicz, J. and Skolimowska, M. (2006). Preservation of classes of life distributions and stochastic orders under weighting, Statistics and Probability Letters, 76, 587-596. crossref(new window)

Belzunce, F., Ortega, E. and Ruiz, J. M. (1999). The Laplace order and ordering of residual lives, Statistics and Probability Letters, 42, 145-156. crossref(new window)

Elbatal, I. (2007). The Laplace order and ordering of reversed residual life, Applied Mathematical Sciences, 36, 1773-1788.

Gastwirth, J. L. (1971). A general definition of the Lorenz curve, Econometrica, 39, 1037-1039. crossref(new window)

Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application, Mathematics and Computers in Simulation, 78, 493-506. crossref(new window)

Glaser, R. E. (1980). Bathtub and related failure rate characterizations, Journal of the American Statistical Association, 75, 667-672. crossref(new window)

Grandell, J. (1997). Mixed Poisson Processes, Chapman and Hall, London.

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. crossref(new window)

Holgate, P. (1970). The modality of some compound Poisson distribution, Biometrika, 57, 666-667. crossref(new window)

Lehmann, E. L. (1955). Ordered families of distributions, Annals of Mathematical Statistics, 26, 399-419. crossref(new window)

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.

Lindley, D. V. (1958). Fiducial distribution and Bayes theorem, Journal of the Royal Statistical Society, 20, 102-107.

Lindley, D. V. (1965). Introduction to Probability and Statistics from a Bayesian Viewpoint, Cambridge University Press, New York.

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. crossref(new window)

Navarro, J. (2008). Likelihood ratio ordering of order statistics, mixtures and systems, Statistical of Planning and Inference, 138, 1242-1257. crossref(new window)

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. crossref(new window)

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

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.

Ross, S. M. (1983). Stochastic Processes, Wiley, New York.

Sankaran, M. (1970). The discrete Poisson-Lindley distribution, Biometrics, 26, 145-149. crossref(new window)

Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders, Springer, New York.