• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.413-430
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• 2020

The multiply Type-II hybrid censoring scheme is disadvantaged by an experiment time that is too long. To overcome this limitation, we propose a generalized multiply Type-II hybrid censoring scheme. Some estimators of the scale parameter of the exponential distribution are derived under a generalized multiply Type-II hybrid censoring scheme. First, the maximum likelihood estimator of the scale parameter of the exponential distribution is obtained under the proposed censoring scheme. Second, we obtain the Bayes estimators under different loss functions with a noninformative prior and an informative prior. We approximate the Bayes estimators by Lindleys approximation and the Tierney-Kadane method since the posterior distributions obtained by the two priors are complicated. In addition, the Bayes estimators are obtained by using the Markov Chain Monte Carlo samples. Finally, all proposed estimators are compared in the sense of the mean squared error through the Monte Carlo simulation and applied to real data.

• 대한수학회논문집
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• 제14권1호
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• pp.121-134
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• 1999

Generalized nonnegative polynomials are defined as the products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We extend some results on Infinite-Finite range inequalities, Christoffel functions, and Nikolski type inequalities corresponding to weights W\ulcorner(x)=exp(-｜x｜\ulcorner), $\alpha$>0, to those for generalized nonnegative polynomials.

• 한국지능시스템학회논문지
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• 제24권4호
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• pp.398-402
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• 2014

일반화된 삼각함수 퍼지집합은 삼각함수 퍼지수의 일반화이다. Zadeh([7])는 확률을 이용하여 퍼지이벤트에 대한 확률을 정의하였다. 우리는 정규분포와 지수분포를 각각 이용하여 실수 $\mathbb{R}$ 위에서 정규퍼지확률과 지수퍼지확률을 정의하고, 일반화된 삼각함수 퍼지집합에 대하여 정규퍼지확률과 지수퍼지확률을 계산하였다.

• 호남수학학술지
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• 제31권3호
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• pp.451-462
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• 2009

In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

• Korean Journal of Mathematics
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• 제20권2호
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• pp.213-223
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• 2012

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.277-288
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• 2010

We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.

• 충청수학회지
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• 제22권1호
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• pp.7-10
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• 2009

With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

• Journal of the Korean Statistical Society
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• 제22권1호
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• pp.55-69
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• 1993

Consider the problem of estimating an arbitrary continuous vector function under a weighted quadratic loss in the multiparameter exponential family with the density of the natural form. We first provide, using Blyth's (1951) method, a set of sufficient conditions for the admisibility of (possibly generalized Bayes) estimators and then treat some examples for normal, Poisson, and gamma distributions as applications of the main result.

• Kyungpook Mathematical Journal
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• 제64권3호
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• pp.395-405
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• 2024

In this paper we define a matrix sequence called the Pell matrix sequence whose elements consist of Pell numbers. Using a positive parameter k, we generalize the Pell matrix sequence to a k-Pell matrix sequence and using two parameters s, t we generalize them to (s, t)-Pell matrix sequences. We give the basic properties of these matrix sequences. Then, using these properties we obtain exponential representations of the Pell matrix sequence and its generalizations in different ways.