IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v003i01.html
   My bibliography  Save this article

Derivatives of the Incomplete Beta Function

Author

Listed:
  • Boik, Robert J.
  • Robinson-Cox, James F.

Abstract

The incomplete beta function is defined as where Beta(p, q) is the beta function. Dutka (1981) gave a history of the development and numerical evaluation of this function. In this article, an algorithm for computing first and second derivatives of Ix,p,q with respect to p and q is described. The algorithm is useful, for example, when fitting parameters to a censored beta, truncated beta, or a truncated beta-binomial model.

Suggested Citation

  • Boik, Robert J. & Robinson-Cox, James F., 1998. "Derivatives of the Incomplete Beta Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 3(i01).
    • Handle: RePEc:jss:jstsof:v:003:i01
    DOI: http://hdl.handle.net/10.18637/jss.v003.i01
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v003i01/beta.der.pdf
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v003i01/beta.der.f
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v003i01/code.zip
    Download Restriction: no
    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v003.i01?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
    ---><---

    References listed on IDEAS

    as
    1. Ram Tripathi & Ramesh Gupta & John Gurland, 1994. "Estimation of parameters in the beta binomial model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 317-331, June.
    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. Cadot, Olivier & Roller, Lars-Hendrik & Stephan, Andreas, 2006. "Contribution to productivity or pork barrel? The two faces of infrastructure investment," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1133-1153, August.
    2. Pi, Jinxiu & Yang, Guanghui & Tang, Wei & Yang, Hui, 2022. "Stochastically stable equilibria for evolutionary snowdrift games with time costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    3. Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.
    4. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    5. Xiang, Qinfang & Edwards, Jode & Gadbury, Gary L., 2006. "Interval estimation in a finite mixture model: Modeling P-values in multiple testing applications," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 570-586, November.

    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. Maria Iannario, 2015. "Detecting latent components in ordinal data with overdispersion by means of a mixture distribution," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 977-987, May.
    2. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    3. Ali Jafari, 2012. "Inferences on the ratio of two generalized variances: independent and correlated cases," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 297-314, August.
    4. Aubry, Philippe & Francesiaz, Charlotte & Guillemain, Matthieu, 2024. "On the impact of preferential sampling on ecological status and trend assessment," Ecological Modelling, Elsevier, vol. 492(C).
    5. Hekimoğlu, Mustafa & Karlı, Deniz, 2023. "Modeling repair demand in existence of a nonstationary installed base," International Journal of Production Economics, Elsevier, vol. 263(C).
    6. Iliopoulos, George, 2008. "UMVU estimation of the ratio of powers of normal generalized variances under correlation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1051-1069, July.
    7. Iliopoulos, George & Kourouklis, Stavros, 1999. "Improving on the Best Affine Equivariant Estimator of the Ratio of Generalized Variances," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 176-192, February.
    8. repec:jss:jstsof:03:i01 is not listed on IDEAS
    9. Dolgui, Alexandre & Pashkevich, Maksim, 2008. "Demand forecasting for multiple slow-moving items with short requests history and unequal demand variance," International Journal of Production Economics, Elsevier, vol. 112(2), pages 885-894, April.
    10. N. Balakrishnan & M. Koutras & F. Milienos, 2014. "Some binary start-up demonstration tests and associated inferential methods," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 759-787, August.
    11. Marcin Blazejowski & Jacek Kwiatkowski, 2023. "BACE: A gretl Package for Model Averaging in Limited Dependent Variable Models," gretl working papers 9, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    12. Jianjun Zhang & Lei Yang & Xianyi Wu, 2019. "Polya tree priors and their estimation with multi-group data," Statistical Papers, Springer, vol. 60(3), pages 849-875, June.

    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:jss:jstsof:v:003:i01. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    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.