IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i3p741-764.html
   My bibliography  Save this article

Moments of truncated normal/independent distributions

Author

Listed:
  • Ali Genç

Abstract

In this work we have considered the problem of finding the moments of a doubly truncated member of the class of normal/independent distributions. We obtained a general result and then use it to derive the moments in the case of doubly truncated versions of Pearson type VII distribution, slash distribution, contaminated normal distribution, double exponential distribution and variance gamma distribution. We also give an application of some actuarial data. Copyright Springer-Verlag 2013

Suggested Citation

  • Ali Genç, 2013. "Moments of truncated normal/independent distributions," Statistical Papers, Springer, vol. 54(3), pages 741-764, August.
  • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:741-764
    DOI: 10.1007/s00362-012-0459-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-012-0459-9
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00362-012-0459-9?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. Nadarajah, Saralees, 2008. "Letter to the editor," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 574-575, March.
    2. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    3. Horrace, William C., 2005. "On ranking and selection from independent truncated normal distributions," Journal of Econometrics, Elsevier, vol. 126(2), pages 335-354, June.
    4. Schott, James R., 2002. "Testing for elliptical symmetry in covariance-matrix-based analyses," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 395-404, December.
    5. Nadarajah, Saralees & Kotz, Samuel, 2008. "Letter to the Editor," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 306-307, February.
    6. Dueker, Michael, 2006. "Kalman filtering with truncated normal state variables for Bayesian estimation of macroeconomic models," Economics Letters, Elsevier, vol. 93(1), pages 58-62, October.
    7. 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.
    8. Apostolos Batsidis, 2012. "Errors of misclassification in discrimination with data from truncated t populations," Statistical Papers, Springer, vol. 53(2), pages 281-298, May.
    9. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    10. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    11. Saralees Nadarajah & Samuel Kotz, 2008. "Moments of truncated t and F distributions," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 7(1), pages 63-73, April.
    12. Nadarajah, Saralees, 2008. "Letter to the Editor," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 1010-1012, May.
    13. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    14. Saralees Nadarajah, 2008. "Reply to the letter to the editor," Computational Statistics, Springer, vol. 23(4), pages 667-668, October.
    15. Burdett, Kenneth, 1996. "Truncated means and variances," Economics Letters, Elsevier, vol. 52(3), pages 263-267, September.
    16. Sakhanenko, Lyudmila, 2008. "Testing for ellipsoidal symmetry: A comparison study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 565-581, December.
    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. Lin, Tsung-I & Wang, Wan-Lun, 2024. "On moments of truncated multivariate normal/independent distributions," Journal of Multivariate Analysis, Elsevier, vol. 199(C).

    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. Franco, Manuel & Vivo, Juana-María, 2010. "A multivariate extension of Sarhan and Balakrishnan's bivariate distribution and its ageing and dependence properties," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 491-499, March.
    2. Ignatieva, Katja & Landsman, Zinoviy, 2015. "Estimating the tails of loss severity via conditional risk measures for the family of symmetric generalised hyperbolic distributions," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 172-186.
    3. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    4. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    5. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2021. "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation," Annals of Operations Research, Springer, vol. 299(1), pages 1281-1315, April.
    6. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    7. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    8. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    9. Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
    10. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    11. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.
    12. Markus Leippold & Nikola Vasiljević, 2020. "Option-Implied Intrahorizon Value at Risk," Management Science, INFORMS, vol. 66(1), pages 397-414, January.
    13. Noureddine Kouaissah & Sergio Ortobelli Lozza & Ikram Jebabli, 2022. "Portfolio Selection Using Multivariate Semiparametric Estimators and a Copula PCA-Based Approach," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 833-859, October.
    14. Kevin Maritato & Stan Uryasev, 2023. "Derivative of Reduced Cumulative Distribution Function and Applications," JRFM, MDPI, vol. 16(10), pages 1-24, October.
    15. Brandtner, Mario, 2018. "Expected Shortfall, spectral risk measures, and the aggravating effect of background risk, or: risk vulnerability and the problem of subadditivity," Journal of Banking & Finance, Elsevier, vol. 89(C), pages 138-149.
    16. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    17. Budhi Surya & Ryan Kurniawan, 2014. "Optimal Portfolio Selection Based on Expected Shortfall Under Generalized Hyperbolic Distribution," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 193-236, September.
    18. Walter Farkas & Ludovic Mathys & Nikola Vasiljević, 2021. "Intra‐Horizon expected shortfall and risk structure in models with jumps," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 772-823, April.
    19. Willmot, Gordon E. & Woo, Jae-Kyung, 2022. "Remarks on a generalized inverse Gaussian type integral with applications," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    20. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.

    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:3:p:741-764. 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.