A view on Bhattacharyya bounds for inverse Gaussian distributions |
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Authors: | G R Mohtashami Borzadaran A H Rezaei Roknabadi M Khorashadizadeh |
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Institution: | 1. Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
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Abstract: | Shanbhag (J Appl Probab 9:580–587, 1972; Theory Probab Appl 24:430–433, 1979) showed that the diagonality of the Bhattacharyya
matrix characterizes the set of Normal, Poisson, Binomial, negative Binomial, Gamma or Meixner hypergeometric distributions.
In this note, using Shanbhag (J Appl Probab 9:580–587, 1972; Theory Probab Appl 24:430–433, 1979) and Pommeret (J Multivar
Anal 63:105–118, 1997) techniques, we evaluated the general form of the 5 × 5 Bhattacharyya matrix in the natural exponential
family satisfying
f(x|q)=\fracexp{xg(q)}b(g(q))y(x){f(x|\theta)=\frac{\exp\{xg(\theta)\}}{\beta(g(\theta))}\psi(x)} with cubic variance function (NEF-CVF) of
θ. We see that the matrix is not diagonal like distribution with quadratic variance function and has off-diagonal elements.
In addition, we calculate the 5 × 5 Bhattacharyya matrix for inverse Gaussian distribution and evaluated different Bhattacharyya
bounds for the variance of estimator of the failure rate, coefficient of variation, mode and moment generating function due
to inverse Gaussian distribution. |
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Keywords: | |
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