Part of the Lecture Notes in Statistics book series (LNS, volume 9)


The subject of the present study is the generalized inverse Gaussian distribution whose probability density function is given by
$$ {\frac{{(\Psi /X)}}{{2{K_{\lambda }}\;(\sqrt {{X\psi }} )}}^{{\frac{\lambda }{2}}}}\;{X^{{\lambda - 1}}}{e^{{ - \frac{1}{2}({X^{{{X^{{ - 1}}}}}} + \psi X)}}}\quad (x > 0), $$
where Kλ is the modified Bessel function of the third kind and with index λ. Special cases of (1.1) are the gamma distribution (χ = 0, λ > 0)> the distribution of a reciprocal gamma variate (ψ = 0, λ < 0) (in the following denoted the reciprocal gamma distribution), the inverse Gaussian distribution (λ =-1/2) and the distribution of a reciprocal inverse Gaussian variate (λ = 1/2). Other important cases are λ = 0 (the hyperbola distribution) and λ = 1.


Probability Density Function Asymptotic Distribution Important Case Close Analogy Positive Variate 
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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  1. 1.Department of MathematicsOdense UniversityOdense MDenmark

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