IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v65y2003i3p269-277.html
   My bibliography  Save this article

Skewed distributions generated by the normal kernel

Author

Listed:
  • Nadarajah, Saralees
  • Kotz, Samuel

Abstract

Following the recent paper by Gupta et al. (Some skew-symmetric models. Random Operators Stochastic Equations 10 (2002) 133) we generate skew probability density functions (pdfs) of the form 2f(u)G([lambda]u), where f is taken to be a normal pdf while the cumulative distributive function G is taken to come from one of normal, Student's t, Cauchy, Laplace, logistic or uniform distribution. The properties of the resulting distributions are studied. In particular, expressions for the nth moment and the characteristic function are derived. We also provide graphical illustrations and quantify the range of possible values of skewness and kurtosis.

Suggested Citation

  • Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:3:p:269-277
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00271-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
    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. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    2. Parisa Hasanalipour & Mostafa Razmkhah, 2021. "Testing skew-symmetry based on extreme ranked set sampling," Statistical Papers, Springer, vol. 62(5), pages 2311-2332, October.
    3. A. Ghalamfarsa Mostofi & M. Kharrati-Kopaei, 2012. "Bayesian nonparametric inference for unimodal skew-symmetric distributions," Statistical Papers, Springer, vol. 53(4), pages 821-832, November.
    4. Krueger, Rico & Rashidi, Taha H. & Vij, Akshay, 2020. "A Dirichlet process mixture model of discrete choice: Comparisons and a case study on preferences for shared automated vehicles," Journal of choice modelling, Elsevier, vol. 36(C).
    5. A. Abtahi & M. Towhidi & J. Behboodian, 2011. "An appropriate empirical version of skew-normal density," Statistical Papers, Springer, vol. 52(2), pages 469-489, May.
    6. Shushi, Tomer, 2018. "Generalized skew-elliptical distributions are closed under affine transformations," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 1-4.
    7. Samuel Kotz & Donatella Vicari, 2005. "Survey of developments in the theory of continuous skewed distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 225-261.
    8. V. Nekoukhou & M. Alamatsaz, 2012. "A family of skew-symmetric-Laplace distributions," Statistical Papers, Springer, vol. 53(3), pages 685-696, August.
    9. Shushi, Tomer, 2018. "A proof for the existence of multivariate singular generalized skew-elliptical density functions," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 50-55.
    10. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2017. "Extended Generalized Skew-Elliptical Distributions and their Moments," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-100, February.
    11. Cabral, Celso Rômulo Barbosa & Bolfarine, Heleno & Pereira, José Raimundo Gomes, 2008. "Bayesian density estimation using skew student-t-normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5075-5090, August.
    12. Saralees Nadarajah, 2009. "Pearson type VII ratio distribution," Empirical Economics, Springer, vol. 37(1), pages 219-229, September.
    13. Clécio da Silva Ferreira & Gilberto A. Paula & Gustavo C. Lana, 2022. "Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors," Computational Statistics, Springer, vol. 37(1), pages 445-468, March.
    14. Rico Krueger & Taha H. Rashidi & Akshay Vij, 2019. "Semi-Parametric Hierarchical Bayes Estimates of New Yorkers' Willingness to Pay for Features of Shared Automated Vehicle Services," Papers 1907.09639, arXiv.org.
    15. Nadarajah Saralees, 2008. "Skewed distributions generated by the Student's t kernel," Monte Carlo Methods and Applications, De Gruyter, vol. 13(5-6), pages 389-404, January.
    16. Huang, Wen-Jang & Chen, Yan-Hau, 2006. "Quadratic forms of multivariate skew normal-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 871-879, May.
    17. Umbach, Dale, 2006. "Some moment relationships for skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 507-512, March.
    18. Shams Harandi, S. & Alamatsaz, M.H., 2013. "Alpha–Skew–Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 774-782.
    19. Sharon Lee & Geoffrey McLachlan, 2013. "Model-based clustering and classification with non-normal mixture distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 427-454, November.
    20. Hossein Negarestani & Ahad Jamalizadeh & Sobhan Shafiei & Narayanaswamy Balakrishnan, 2019. "Mean mixtures of normal distributions: properties, inference and application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 501-528, May.
    21. Tu, Shiyi & Wang, Min & Sun, Xiaoqian, 2016. "Bayesian analysis of two-piece location–scale models under reference priors with partial information," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 133-144.
    22. Saralees Nadarajah, 2010. "On the distribution of Harter," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(3), pages 565-572, April.
    23. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.

    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. Shakhatreh, M.K., 2012. "A two-parameter of weighted exponential distributions," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 252-261.
    2. Hok Shing Kwong & Saralees Nadarajah, 2022. "A New Robust Class of Skew Elliptical Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1669-1691, September.
    3. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    4. Fang, B. Q., 2003. "The skew elliptical distributions and their quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 298-314, November.
    5. S. Cabras & M. E. Castellanos, 2009. "Default Bayesian goodness-of-fit tests for the skew-normal model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 223-232.
    6. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.
    7. Alessandra Durio & Yacov Yu. Nikitin, 2001. "Local asympotic efficiency of some goodness-of-fit tests under skew alternatives," ICER Working Papers 04-2001, ICER - International Centre for Economic Research.
    8. Vanduffel, Steven & Yao, Jing, 2017. "A stein type lemma for the multivariate generalized hyperbolic distribution," European Journal of Operational Research, Elsevier, vol. 261(2), pages 606-612.
    9. Alessandra Durio & Yakov Nikitin, 2002. "Asympotic efficiency of signed - rank symmetry tests under skew alternatives," ICER Working Papers 12-2002, ICER - International Centre for Economic Research.
    10. Mahdy Mervat Mahdy Ramadan, 2011. "A Class of Weighted Gamma Distributions and its Properties," Stochastics and Quality Control, De Gruyter, vol. 26(2), pages 133-144, January.
    11. Behboodian, J. & Jamalizadeh, A. & Balakrishnan, N., 2006. "A new class of skew-Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1488-1493, August.
    12. Chung-Shin Liu & Meng-Shiuh Chang & Ximing Wu & Chin Man Chui, 2016. "Hedges or safe havens—revisit the role of gold and USD against stock: a multivariate extended skew- copula approach," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1763-1789, November.
    13. Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
    14. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 389-401, June.
    15. Zaid Mundher, 2022. "A Method for Investigating Coverage Area Issue in Dynamic Networks," Technium, Technium Science, vol. 4(1), pages 19-27.
    16. Yulia V. Marchenko & Marc G. Genton, 2010. "A suite of commands for fitting the skew-normal and skew-t models," Stata Journal, StataCorp LP, vol. 10(4), pages 507-539, December.
    17. Huang, Wen-Jang & Chen, Yan-Hau, 2006. "Quadratic forms of multivariate skew normal-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 871-879, May.
    18. Jose, K.K. & Naik, Shanoja R., 2008. "A class of asymmetric pathway distributions and an entropy interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(28), pages 6943-6951.
    19. Fang, B.Q., 2008. "Noncentral matrix quadratic forms of the skew elliptical variables," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1105-1127, July.
    20. Umbach, Dale, 2006. "Some moment relationships for skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 507-512, March.

    More about this item

    Statistics

    Access and download statistics

    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:eee:stapro:v:65:y:2003:i:3:p:269-277. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.