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Inference of Stress-Strength Model for a Lomax Distribution

Authors: H. Panahi, S. Asadi


In this paper, the estimation of the stress-strength parameter R = P(Y < X), when X and Y are independent and both are Lomax distributions with the common scale parameters but different shape parameters is studied. The maximum likelihood estimator of R is derived. Assuming that the common scale parameter is known, the bayes estimator and exact confidence interval of R are discussed. Simulation study to investigate performance of the different proposed methods has been carried out.

Keywords: stress-strength model, Bayes estimator, maximum likelihoodestimator, Lomax distribution

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[1] D. Kundu, and R.D. Gupta, "Estimation of P(Y < X) for Generalized Exponential Distribution," Metrika, vol. 61(3), 2005, pp. 291-308.
[2] J.G. Surles, and W.J. Padgett, (1998), "Inference for P(Y < X) in the Burr Type X,model," Journal of Applied Statistical Science, 1998, pp. 225-238.
[3] H. Panahi and S. Asadi, "Estimation of R=P
[Y < X] for two-parameter Burr Type XII Distribution," World Academy of Science, Engineering and Technology, vol. 72, pp. 465-470, 2010.
[4] A.M. Awad, and M.K. Gharraf, "Estimation of P(Y[5] M.Z. Raqab, and D. Kundu, "Comparison of different estimators of P(Y < X),for a scaled Burr Type X distribution," Communications in Statistics - Simulation and Computation, vol. 34(2), 2005, 465-483.
[6] N.A. Mokhlis, "Reliability of a Stress-Strength Model with Burr Type III Distributions," Communications in StatisticsÔÇöTheory and Methods, vol. 34, 2005, pp. 1643-1657.
[7] J. G. Surles, and W. J. Padgett, "Inference for P(Y < X) in the Burr type X model," Applied Statistics Science, vol, 7, 2001, pp. 225-238.
[8] H. S. Lomax, "Business Failures; Another example of the analysis of failure data," JASA, vol. 49, 1954, pp. 847-852.
[9] M. E. Ghitany, F. A. Al-Awadhi and L. A. Alkhalfan, "Marshall-Olkin Extended Lomax Distribution and Its Application to Censored Data," Communications in Statistics - Theory and Methods, vol. 36, 2007, pp. 1855-1866.
[10] S. Nadarajah, "Sums, products, and ratios for the bivariate lomax distribution," Computational Statistics & Data Analysis, vol. 49, 2005, pp. 109-129.
[11] S. K. Mohamed and A. M. Abd-Elfattah, "Parameter Estimation of The Hybrid Censored Lomax Distribution" Pakistan Journal of Statistics and Operation Research, vol. 7, 2011.
[12] A.H. Aharby, "A Study on Lomax Distribution as a Life Testing Model," The Scientific Journal for Economic and Commerce, vol. 3, 2003.
[13] G.S. Rao, "On Sample Size Estimation For Lomax Disrtibution," Australian Journal of Basic and Applied Sciences, vol. 1, 2007, pp. 373- 378.
[14] D.V. Lindley, (1980). "Approximate Bayesian methods," Trabajos de Estadistica, vol, 3, 1980, pp. 281-288.