IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i2p499-522.html
   My bibliography  Save this article

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

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-012-0446-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-012-0446-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. M. Mahdizadeh & Ehsan Zamanzade, 2018. "A new reliability measure in ranked set sampling," Statistical Papers, Springer, vol. 59(3), pages 861-891, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel J. Luckett & Eric B. Laber & Samer S. El‐Kamary & Cheng Fan & Ravi Jhaveri & Charles M. Perou & Fatma M. Shebl & Michael R. Kosorok, 2021. "Receiver operating characteristic curves and confidence bands for support vector machines," Biometrics, The International Biometric Society, vol. 77(4), pages 1422-1430, December.
    2. Y. Huang & M. S. Pepe, 2009. "A Parametric ROC Model-Based Approach for Evaluating the Predictiveness of Continuous Markers in Case–Control Studies," Biometrics, The International Biometric Society, vol. 65(4), pages 1133-1144, December.
    3. Beom Seuk Hwang & Zhen Chen, 2015. "An Integrated Bayesian Nonparametric Approach for Stochastic and Variability Orders in ROC Curve Estimation: An Application to Endometriosis Diagnosis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 923-934, September.
    4. Jin, Hua & Lu, Ying, 2009. "The ROC region of a regression tree," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 936-942, April.
    5. Holly Janes & Margaret S. Pepe, 2008. "Matching in Studies of Classification Accuracy: Implications for Analysis, Efficiency, and Assessment of Incremental Value," Biometrics, The International Biometric Society, vol. 64(1), pages 1-9, March.
    6. M. J. S. Khan & Bushra Khatoon, 2020. "Statistical Inferences of $$R=P(X," Annals of Data Science, Springer, vol. 7(3), pages 525-545, September.
    7. Ziyi Li & Yijian Huang & Dattatraya Patil & Martin G. Sanda, 2023. "Covariate adjustment in continuous biomarker assessment," Biometrics, The International Biometric Society, vol. 79(1), pages 39-48, March.
    8. Luca Greco & Laura Ventura, 2011. "Robust inference for the stress–strength reliability," Statistical Papers, Springer, vol. 52(4), pages 773-788, November.
    9. Soutik Ghosal & Zhen Chen, 2022. "Discriminatory Capacity of Prenatal Ultrasound Measures for Large-for-Gestational-Age Birth: A Bayesian Approach to ROC Analysis Using Placement Values," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(1), pages 1-22, April.
    10. Lori E. Dodd & Margaret S. Pepe, 2003. "Partial AUC Estimation and Regression," Biometrics, The International Biometric Society, vol. 59(3), pages 614-623, September.
    11. Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    12. Holly Janes & Gary Longton & Margaret S. Pepe, 2009. "Accommodating covariates in receiver operating characteristic analysis," Stata Journal, StataCorp LP, vol. 9(1), pages 17-39, March.
    13. Y. L. Lio & Tzong-Ru Tsai, 2012. "Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 309-322, April.
    14. Filippo Domma & Sabrina Giordano, 2013. "A copula-based approach to account for dependence in stress-strength models," Statistical Papers, Springer, vol. 54(3), pages 807-826, August.
    15. William M. Briggs & Russell Zaretzki, 2008. "The Skill Plot: A Graphical Technique for Evaluating Continuous Diagnostic Tests," Biometrics, The International Biometric Society, vol. 64(1), pages 250-256, March.
    16. Rodríguez-Álvarez, María Xosé & Roca-Pardiñas, Javier & Cadarso-Suárez, Carmen, 2011. "A new flexible direct ROC regression model: Application to the detection of cardiovascular risk factors by anthropometric measures," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3257-3270, December.
    17. Abhimanyu Singh Yadav & S. K. Singh & Umesh Singh, 2019. "Bayesian estimation of $$R=P[Y," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 905-917, October.
    18. Ali Genç, 2013. "Moments of truncated normal/independent distributions," Statistical Papers, Springer, vol. 54(3), pages 741-764, August.
    19. Rafael Villa & Marta Serrano & Tomás García & Gema González, 2023. "To Green or Not to Green: The E-Commerce-Delivery Question," Sustainability, MDPI, vol. 15(16), pages 1-21, August.
    20. Kelly Zou & W. J. Hall, 2002. "Semiparametric and parametric transformation models for comparing diagnostic markers with paired design," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(6), pages 803-816.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:499-522. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.