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Orthogonal Functions of Inverse Gaussian Distributions

In: Lifetime Data: Models in Reliability and Survival Analysis

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  • Ryuei Nishii

    (Hiroshima University, Faculty of Integrated Arts and Sciences)

Abstract

The univariate natural exponential families with quadratic variance functions have the orthogonal polynomial systems which are generated by differentiating the densities. This method, however, is not applicable to inverse Gaussian distributions because their variance functions are cubic. We will generate non-orthogonal but simple polynomials and orthogonal functions of inverse Gaussian distributions based on Laguerre polynomials. Properties of the polynomials and the functions are obtained by the use of the generating functions. They are applied to approximate a lognormal density and examined numerically.

Suggested Citation

  • Ryuei Nishii, 1996. "Orthogonal Functions of Inverse Gaussian Distributions," Springer Books, in: Nicholas P. Jewell & Alan C. Kimber & Mei-Ling Ting Lee & G. A. Whitmore (ed.), Lifetime Data: Models in Reliability and Survival Analysis, pages 243-250, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-5654-8_32
    DOI: 10.1007/978-1-4757-5654-8_32
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