H. Dinges, Special cases of second order Wiener germ approximations, Probability Theory and Related Fields, 83:5--57 (1989). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Asymptotic Estimates of Elementary Probability Distributions - Hwang (2 citations) (Correct)
....2.2. Let us first list some known asymptotic estimates of #m (#) in the literature. They are not intended to be complete but are chosen according to the variation of the second parameter m. For more information on other types of approximations, see the monographs [20, 31, 25, 5] the articles [2, 13] and the less known (in probability literature) article by Norton [32] where a rather complete account (before 1976) on asymptotics of #m (#) is given. Henceforth, #(x) denotes the standard normal distribution function: #(x) e t dt (x R) 1. The classical central limit theorem (cf. ....
....while when m = # o(#) it is characterized by Cramer type large deviations. 2. When m Temme s expansion (3) is useful. 3. In the ranges 0 # # or m # A # #, A 0, our results can be used. Many other types of normal approximation (usually of the form #m (#) #(g(#, m) can be found in [31, 2, 13]. Concerning the case when m and # bounded, we have by the saddlepoint method (cf. 50] e # m r m 1 # 2#m # 12# 12m 288# 888# 313 where r = m # 1. Note that this expansion can also be obtained from (3) but with more involved computations. 2.3 Poissonization ....
[Article contains additional citation context not shown here]
H. Dinges, Special cases of second order Wiener germ approximations, Probability Theory and Related Fields, 83:5--57 (1989).
Asymptotic Estimates of Elementary Probability Distributions - Hwang (1996) (2 citations) (Correct)
....x 2.2. Let us first list some known asymptotic estimates of Pi m ( in the literature. They are not intended to be complete but are chosen according to the variation of the second parameter m. For more information on other types of approximations, see the monographs [20, 31, 25, 5] the papers [2, 13] and the less known (in probability literature) paper by Norton [32] where a rather complete account (before 1976) on asymptotics of Pi m ( is given. Henceforth, Phi(x) denotes the standard normal distribution function: Phi(x) Z x dt (x 2 R) 1. The classical central limit ....
....= o( it is characterized by Cram er type large deviations. 2. When m 1, Temme s expansion (3) is useful. 3. In the ranges 0 m Gamma A or m A , A 0, our results can be used. Many other types of normal approximation (usually of the form Pi m ( Phi(g( m) can be found in [31, 2, 13]. Concerning the case when m 1 and bounded, we have by the saddle point method (cf. 50] 12 Gamma 13 12m 288 Gamma 888 313 where r = m= 1. Note that this expansion can also be obtained from (3) but with more involved computations. 2.3 Poissonization ....
[Article contains additional citation context not shown here]
H. Dinges, Special cases of second order Wiener germ approximations, Probability Theory and Related Fields, 83:5--57 (1989).
A Wiener Germ Approximation of the Noncentral Chi Square.. - Penev, Raykov (Correct)
....parameter is around 190 or larger. Our goal is to suggest and promote another algorithm for a simple and very precise approximation of the cdf and quantiles of the noncentral 2 distribution. It is based on the second order Wiener germ approximation to the cdf. Theoretical account is given in Dinges (1989). The notion of a Wiener germ seems not to be widely known amongst applied statisticians who are much more acquainted with the saddlepoint approximation (Daniels (1987) for tail areas. In fact, the first order Wiener germ approximation has the same asymptotic order of the error like the well ....
....not to be widely known amongst applied statisticians who are much more acquainted with the saddlepoint approximation (Daniels (1987) for tail areas. In fact, the first order Wiener germ approximation has the same asymptotic order of the error like the well known Lugannani Rice approximation (see Dinges (1989)) The second order Wiener germ approximation brings about a small further improvement. The advantage of the Wiener germ approximation formulae is that the former always give a probability (a value in (0,1) and that for its calculation only one call of the 3 cdf of the standard normal is ....
[Article contains additional citation context not shown here]
Dinges, H. (1989), ' Special cases of second order Wiener germ approximations ', Probability Theory and Related Fields, 83, 5--57.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC