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The simplicity of likelihood based inferences for P(X > Y) and for the ratio of means in the exponential model

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  • Eloísa Díaz-Francés
  • José Montoya

Abstract

The profile likelihood of the reliability parameter θ = P(X > Y) or of the ratio of means, when X and Y are independent exponential random variables, has a simple analytical expression and is a powerful tool for making inferences. Inferences about θ can be given in terms of likelihood-confidence intervals with a simple algebraic structure even for small and unequal samples. The case of right censored data can also be handled in a simple way. This is in marked contrast with the complicated expressions that depend on cumbersome numerical calculations of multidimensional integrals required to obtain asymptotic confidence intervals that have been traditionally presented in scientific literature. Copyright Springer-Verlag 2013

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  • Eloísa Díaz-Francés & José Montoya, 2013. "The simplicity of likelihood based inferences for P(X > Y) and for the ratio of means in the exponential model," Statistical Papers, Springer, vol. 54(2), pages 499-522, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:499-522
    DOI: 10.1007/s00362-012-0446-1
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    References listed on IDEAS

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    1. L. Jiang & A. Wong, 2008. "A note on inference for P(X > Y) for right truncated exponentially distributed data," Statistical Papers, Springer, vol. 49(4), pages 637-651, October.
    2. Margaret Sullivan Pepe, 2000. "An Interpretation for the ROC Curve and Inference Using GLM Procedures," Biometrics, The International Biometric Society, vol. 56(2), pages 352-359, June.
    3. Debasis Kundu & Rameshwar D. Gupta, 2005. "Estimation of P[Y > X] for generalized exponential distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 291-308, June.
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    Cited by:

    1. M. Mahdizadeh & Ehsan Zamanzade, 2018. "A new reliability measure in ranked set sampling," Statistical Papers, Springer, vol. 59(3), pages 861-891, September.
    2. Sumith Gunasekera, 2015. "Generalized inferences of $$R$$ R = $$\Pr (X>Y)$$ Pr ( X > Y ) for Pareto distribution," Statistical Papers, Springer, vol. 56(2), pages 333-351, May.
    3. Ali Dastbaravarde & Ehsan Zamanzade, 2020. "On estimation of $$P\left( X > Y \right) $$PX>Y based on judgement post stratification," Statistical Papers, Springer, vol. 61(2), pages 767-785, April.

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