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On asymptotic expansion of posterior distribution [PDF]
Lobachevskii Journal of Mathematics, 2016 © 2016, Pleiades Publishing, Ltd.The paper suggests a new asymptotic expansion of posterior distribution, which improves the known normal asymptotic.
A A Zaikin
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Journal of the London Mathematical Society, 1949
Die Differentialgleichung der Bessel-Funktionen wird durch die Transformation \(w = \sqrt{\zeta} J_\nu(\lambda\sqrt{1-\zeta^2})\), \(u = \mathfrak{ArTg}\,\zeta - \zeta\) in die Form gebracht: \[ d^2w/du^2 + w\{- \nu^2 + (\zeta^{-2} - 1) [\tfrac54 \zeta^{-4}+ \tfrac14 \zeta^{-2} + \lambda^2 - \nu^2)]\} = 0, \tag{1} \] wo \(\lambda\) eine geeignet ...
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Die Differentialgleichung der Bessel-Funktionen wird durch die Transformation \(w = \sqrt{\zeta} J_\nu(\lambda\sqrt{1-\zeta^2})\), \(u = \mathfrak{ArTg}\,\zeta - \zeta\) in die Form gebracht: \[ d^2w/du^2 + w\{- \nu^2 + (\zeta^{-2} - 1) [\tfrac54 \zeta^{-4}+ \tfrac14 \zeta^{-2} + \lambda^2 - \nu^2)]\} = 0, \tag{1} \] wo \(\lambda\) eine geeignet ...
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A Uniform Asymptotic Expansion for Krawtchouk Polynomials
Journal of Approximation Theory, 2000 We study the asymptotic behavior of the Krawtchouk polynomial K(N)n(x; p, q) as n→∞. With x≡λN and ν=n/N, an infinite asymptotic expansion is derived, which holds uniformly for λ and ν in compact subintervals of (0, 1).
Li, X.-C., Wong, R.
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On Multivariable Asymptotic Expansions
SIAM Review, 1971In this paper we consider the damped linear oscillator with small damping $\varepsilon $. We obtain uniform asymptotic expansions of the solution as $\varepsilon \to 0$ that are uniformly valid for all time $t \geqq 0$, by the multitime method. We show how to determine the expansion coefficients without resorting to intuitive arguments. This is done by
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Asymptotic expansions at work.
Insurance: Mathematics and Economics, 1995Abstract 1. NORMAL APPROXIMATIONS It is routine among applied statisticians to use normal approximations. One of the most classical results being for the maximum likelihood estimate θ^ based on n i.i.d. observations from a density with expected information i(θ).
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2017
In this chapter, we relax the homogeneous portfolio assumption, and we derive an asymptotic series expansion of the \(k{\text {th}}\)-to-default Q-factor in the non-homogeneous case. We also show how to compute the conditional aggregate default distributions that appear in the expansion using the convolution recursion algorithm.
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In this chapter, we relax the homogeneous portfolio assumption, and we derive an asymptotic series expansion of the \(k{\text {th}}\)-to-default Q-factor in the non-homogeneous case. We also show how to compute the conditional aggregate default distributions that appear in the expansion using the convolution recursion algorithm.
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Asymptotic expansion for splines
1983The author extends some of the previous results on asymptotic expansions for interpolating splines obtained by \textit{T. R. Lucas} [SIAM J. Numer. Anal. 19, 1051-1066 (1982; Zbl 0519.41010)] and the author himself [Sci. Sin., Ser. A 26, 919-930 (1983; Zbl 0524.41006)].
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Mathematical Proceedings of the Cambridge Philosophical Society, 1928
In the theory of the specific heats of gases of diatomic molecules the functionplays a well-known and important part. The rotational specific heat Crot of a diatomic molecule, which is susceptible of representation as a rigid body with two equal principal moments of inertia, without spin about the other principal axis, is given bywhere R is the gram ...
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In the theory of the specific heats of gases of diatomic molecules the functionplays a well-known and important part. The rotational specific heat Crot of a diatomic molecule, which is susceptible of representation as a rigid body with two equal principal moments of inertia, without spin about the other principal axis, is given bywhere R is the gram ...
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Normal Approximations and Asymptotic Expansions.
Journal of the American Statistical Association, 1977Marius Iosifescu +2 more
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An Asymptotic Expansion for the Distribution of a Statistic Admitting an Asymptotic Expansion
Theory of Probability & Its Applications, 1973openaire +1 more source