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A Goodness‐of‐fit Test for Exponentiality Based on the Memoryless Property

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  • Ibrahim A. Ahmad
  • Ibrahim A. Alwasel

Abstract

In this investigation a test of goodness of fit for exponentiality is proposed. This procedure applies equally whether the scale and/or the location parameters of the distribution are known or not. The limiting null and non‐null distributions of the test statistic are normal under minimal conditions. Monte Carlo critical values for small sample sizes are given and the power of the test is calculated for various alternatives showing that it compares favourably relatively to other more complicated published procedures.

Suggested Citation

  • Ibrahim A. Ahmad & Ibrahim A. Alwasel, 1999. "A Goodness‐of‐fit Test for Exponentiality Based on the Memoryless Property," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 681-689.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:3:p:681-689
    DOI: 10.1111/1467-9868.00200
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    Cited by:

    1. Jovanović, Milan & Milošević, Bojana & Nikitin, Ya. Yu. & Obradović, Marko & Volkova, K. Yu., 2015. "Tests of exponentiality based on Arnold–Villasenor characterization and their efficiencies," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 100-113.
    2. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2005. "Bootstrapping modified goodness-of-fit statistics with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 111-121, February.
    3. Zeinab H. Amin, 2007. "Tests for the Validity of the Assumption that the Underlying Distribution of Life is Pareto," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(2), pages 195-201.
    4. Ahmad, Ibrahim A. & Sepehrifar, Mohammad B., 2009. "On testing alternative classes of life distribution with guaranteed survival times," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 857-864, February.
    5. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Other publications TiSEM 402576fa-8c0e-45e2-a394-8, Tilburg University, School of Economics and Management.
    6. Bojana Milošević & Marko Obradović, 2016. "Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 413-427, June.
    7. Mohamed Kayid & Mansour Shrahili, 2023. "Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis," Mathematics, MDPI, vol. 11(6), pages 1-15, March.

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