• 대한수학회보
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• 제38권1호
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• pp.1-6
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• 2001

We discuss the value distribution of composite entire functions including those of infinite order and estimate the number of Q-points of such functions for an entire function Q or relatively slower growth.

• 대한수학회지
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• 제44권4호
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• pp.835-844
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• 2007

This paper considers the problem of estimating the error distribution function in nonparametric regression models. Sufficient conditions are given under which the kernel estimator of the error distribution function based on nonparametric residuals satisfies the law of iterated logarithm.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.747-757
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• 2005

A physical variable is customarily thought of as a function. Another way of describing a physical variable is to specify it as a functional, whose special type is called a distribution. It turns out that the distribution concept provide a better mechanism for analyzing certain physical phenomena than does the function concept. By using wavelets with high regularity we give a resolution of functions with slow growth.

• 충청수학회지
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• 제26권2호
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• pp.269-273
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• 2013

We prove a characterization of the power function distribution by lower record values. We prove that $F(x)=(\frac{x}{a})^{\alpha}$ for all $x$, 0 < $x$ < $a$, ${\alpha}$ > 0 and $a$ > 0 if and only if $\frac{X_{L(n)}}{X_{L(m)}}$ and $X_{L(m)}$ are independent for $1{\leq}m$ < $n$.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.541-547
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• 2009

We consider distribution, reliability and moment of ratio in two independent beta random variables X and Y, and reliability and $K^{th}$ moment of ratio are represented by a mathematical generalized hypergeometric function. We introduce an approximate maximum likelihood estimate(AML) of reliability and right-tail probability in the beta distribution.

• East Asian mathematical journal
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• 제34권3호
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• pp.287-293
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• 2018

We investigate the averaging value of a random sampling ${\zeta}(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our result is that if $X_t$ is an increasing random sampling with Poisson distribution, then $${\mathbb{E}}{\zeta}(1/2+iX_t)=O({\sqrt{\;log\;t}}$$, for all sufficiently large t in ${\mathbb{R}}$.

• 한국조명전기설비학회:학술대회논문집
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• 한국조명전기설비학회 1989년도 추계학술발표회논문집
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• pp.19-24
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• 1989

The electron energy distribution function in mercury discharge positive columns are calculated numerically from the Boltzmann eqation under a set of parameters, such as the electron temperature to. the atomic temperature Tw. the electron number density no. and the electric field E. Especially, using the approximation that collision cross sections only depend on the energy, the calculated electron energy distribution function was shown that it falls off rapidly in the high energy tail.

• Journal of the Korean Data and Information Science Society
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• 제22권2호
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• pp.361-369
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• 2011

In this paper, we develop the reference and the matching priors for the reliability function of two-parameter exponential distribution. We derive the reference priors and the matching prior, and prove the propriety of joint posterior distribution under the general prior including the reference priors and the matching prior. Through the sim-ulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.

• 한국국방경영분석학회지
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• 제9권2호
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• pp.39-43
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• 1983

In this paper, we derive the likelihood function for the independent random order statistic whose underlying lifetime distribution is a two parameter Weibull form. For this purpose we first discuss the order statistic which represent a characteristic feature of most life and fatigue tests that they give rise to ordered observations. And, we describe the properties of the underlying Weibull model. The derived likelihood function is essential for establishing the statistical life test plans in the case of Weibull distribution using a likelihood ratio method.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1335-1344
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• 2008

The maximum likelihood method does not admit explicit solutions when the sample is multiply censored and progressive censored. So we shall propose some approximate maximum likelihood estimators (AMLEs) of the scale parameter for the power function distribution based on multiply Type-II censored samples and progressive Type-II censored samples when shape parameter is known. We compare the proposed estimators in the sense of the mean squared error (MSE) through Monte Carlo simulation for various censoring schemes.