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Testing Exponentiality Against NBUL Alternatives Using Positive and Negative Fractional Moments

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  • Anis M. Z.

    (SQC & OR Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700 108, India.)

Abstract

In this note a moment inequality for the New is Better than Used in Laplace ordering (NBUL) class of lifetime distributions is derived. A simple test statistic for testing exponentiality against NBUL alternatives is constructed. The test statistic is proved to be asymptotically normal and consistent. Critical values obtained by a Monte Carlo simulation are tabulated for different sample sizes. The asymptotic relative efficiency of the test is also studied.

Suggested Citation

  • Anis M. Z., 2011. "Testing Exponentiality Against NBUL Alternatives Using Positive and Negative Fractional Moments," Stochastics and Quality Control, De Gruyter, vol. 26(2), pages 215-234, January.
    • Handle: RePEc:bpj:ecqcon:v:26:y:2011:i:2:p:215-234:n:12
    DOI: 10.1515/EQC.2011.020
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    References listed on IDEAS

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    1. L. Diab, 2010. "Testing for NBUL using goodness of fit approach with applications," Statistical Papers, Springer, vol. 51(1), pages 27-40, January.
    2. Denuit, Michel, 2001. "Laplace transform ordering of actuarial quantities," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 83-102, August.
    3. M. Z. Anis & M. Mitra, 2005. "A simple test of exponentiality against NWBUE family of life distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 21(1), pages 45-53, January.
    4. Khuri A. & Casella G., 2002. "The Existence of the First Negative Moment Revisited," The American Statistician, American Statistical Association, vol. 56, pages 44-47, February.
    5. Belzunce, Félix & Ortega, Eva & Ruiz, José M., 1999. "The Laplace order and ordering of residual lives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 145-156, April.
    6. A. D. Joffe, 1964. "Mixed Exponential Estimation by the Method of Half Moments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 13(2), pages 91-98, June.
    7. Anis M. Z. & Hoque Z., 2008. "On The Performance of A New Test of Exponentiality Against IFR Alternatives Based on the L-statistic Approach," Stochastics and Quality Control, De Gruyter, vol. 23(2), pages 181-195, January.
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