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Fitting Density Functions with Polynomials

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  • Stephen T. Buckland

Abstract

A robust procedure is developed for estimating density functions from data. It requires the existence of a parametric function, called the key function, to give a first approximation to the density and then improves the fit using polynomial adjustments. When the key function is the normal density, Hermite polynomials may be used; similarly, Laguerre polynomials might be preferred if the key is negative exponential. However, adequacy of fit is little affected by choice of polynomials, and it is more straightforward to use simple polynomials whatever the form of the key. Short examples illustrate the wide applicability of the technique. The methodology was developed to allow valid analysis of migration count data for the California grey whale, and this example is considered in detail.

Suggested Citation

  • Stephen T. Buckland, 1992. "Fitting Density Functions with Polynomials," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 63-76, March.
    • Handle: RePEc:bla:jorssc:v:41:y:1992:i:1:p:63-76
    DOI: 10.2307/2347618
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    Cited by:

    1. Tiago Marques & Stephen Buckland & Regina Bispo & Brett Howland, 2013. "Accounting for animal density gradients using independent information in distance sampling surveys," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 67-80, March.
    2. Nora Saadi & Smail Adjabi & Ali Gannoun, 2018. "The selection of the number of terms in an orthogonal series cumulative function estimator," Statistical Papers, Springer, vol. 59(1), pages 127-152, March.
    3. Alberts, T. & Karunamuni, R. J., 2003. "A semiparametric method of boundary correction for kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 287-298, February.
    4. David L. Borchers & Tiago A. Marques, 2017. "From distance sampling to spatial capture–recapture," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 475-494, October.

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