• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.147-153
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• 2007

In this note, we obtained results related to multiparameter discrete exponential families on considering lattice or semi-lattice in place of N (Natural numbers) in view of Cacoullos-type inequalities via the same arguments in Papathanasiou (1990, 1993).

• 대한수학회지
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• 제39권4호
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• pp.495-507
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• 2002

In this paper, the characterization results related to Chernoff-type inequalities are applied for exponential-type (continuous and discrete) families. Upper variance bound is obtained here with a slightly different technique used in Alharbi and Shanbhag [1] and Mohtashami Borzadaran and Shanbhag [8]. Some results are shown with assuming measures such as non-atomic measure, atomic measure, Lebesgue measure and counting measure as special cases of Lebesgue-Stieltjes measure. Characterization results on power series distributions via Chernoff-type inequalities are corollaries to our results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.97-104
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• 1997

The large deviations theorem of Cramer is extended to conditional probabilities in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. The probability that the first falls outside a certain convex set given that the second is fixed is shown to decrease with the sample size at an exponential rate which depends on the Kullback-Leibler distance between two distributions in an associated exponential familiy of distributions. Examples are given which include a method of computing the Bahadur exact slope for tests of certain composite hypotheses in exponential families.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• 응용통계연구
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• 제8권1호
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• pp.133-149
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• 1995

파워(>2)분산함수를 가진 자연지수계열군에 속하는 분포들의 확률밀도함수는 무한급수로 표현되기 때문에 분포들의 유용성에도 불구하고 취급하기가 매우 힘들다. 따라서 이 논문에서는 분포들에 대한 백분위수들의 표를 제시하고자 하였다. 확률밀도 함수의 형태때문에 계산하기 곤란했던 몇가지 백분위수들이 위 분포들이 가지는 확률적 성질들에 기인하여 구해지는 근사백분위수에 의해 상당히 잘 대체될 수 있음을 보여주었다.

• Journal of the Korean Statistical Society
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• 제10권
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• pp.128-139
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• 1981

The Bayesian sequential estimation problem for k parameters exponential families is considered using loss related to the Fisher information. Tractable expressions for the Bayes estimator and the posterior expected loss are found, and the myopic or one-step-ahead stopping rule is defined. Sufficient conditions are given for optimality of the myopic procedure, and the myopic procedure is shown to be asymptotically optimal in all cases considered.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.743-758
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• 2005

This paper consider penalized likelihood regression with data from exponential family. The fast computation method applied to Gaussian data(Kim and Gu, 2004) is extended to non Gaussian data through asymptotically efficient low dimensional approximations and corresponding algorithm is proposed. Also smoothing parameter selection is explored for various exponential families, which extends the existing cross validation method of Xiang and Wahba evaluated only with Bernoulli data.

• 한국해안해양공학회:학술대회논문집
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• 한국해안해양공학회 1992년도 정기학술강연회 발표논문 초록집
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• pp.150-156
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• 1992

수치모델(e.g., Cartons et al., 1976)로 다방향 스펙트라를 예측하여 폭풍에 의한 스펙트라의 다방향성을 제시하여 왔다. apr시코 만에서 얻어진 현장 관측치에 근거하여 연구자들이(Niedzwecki and Whatley, 1991) 다방향 스펙트라를 cosine power, exponential and exponential series families 로 구성된 다방향 방향분산 함수를 제시함에 따라 삼차원적 해양 수치모델을 수립할 수 있으며 이 함수의 다양한 분산 parameter에 의한 다방향 불규칙 파랑의 물입자 흐름을 예측함에 따라 실제적인 계류 시스템의 반응을 검사하였다.(중략)

• 대한수학회지
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• 제48권2호
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• pp.267-288
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• 2011

In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group $SO^-$(2n, q). Here q is a power of three. Then we obtain four infinite families of recursive formulas for power moments of Kloosterman sums with square arguments and four infinite families of recursive formulas for even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups $O^-$(2n, q).

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.275-283
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• 1999

In order to estimate a parameter $(\alpha,\beta^r), r\epsilonN$, in a distribution belonging to a location-scale family we usually use best invariant estimator (BIE) and best unbiased estimator (BUE). But in some conditions Ryu (1996) showed that BIE is better than BUE. In this paper we calculate risks of BIE and BUE in a normal and an exponential distribution respectively and calculate a percentage risk improvement exponential distribution respectively and calculate a percentage risk improvement (PRI). We find the sample size n which make no significant differences between BIE and BUE in a normal distribution. And we show that BIE is always significantly better than BUE in an exponential distribution. Also simulation in a normal distribution is given to convince us of our result.