• 충청수학회지
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• 제30권3호
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• pp.337-340
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• 2017

In this article, we present characterizations of the power distribution via the identical hazard rate of lower record values that $X_n$ has the power distribution if and only if for some fixed n, $n{\geq}1$, the hazard rate $h_W$ of $W=X_{L(n+1)}/X_{L(n)}$ is the same as the hazard rate h of $X_n$ or the hazard rate $h_V$ of $V=X_{L(n+2)}/X_{L(n+1)}$.

• 대한수학회논문집
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• 제10권2호
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• pp.409-417
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• 1995

We consider the $R^k$-valued $(k \geq 1)$ process ${X_n}$ generated by $X_n + 1 = f(X_n)+e_{n+1}$, where $f(x) = (h(x),x^{(1)},x^{(1)},\cdots,x{(k-1)})'$. We assume that h is a real-valued measuable function on $R^k$ and that $e_n = (e'_n,0,\cdot,0)'$ where ${e'_n}$ are independent and identically distributed random variables. We obtained a practical criteria guaranteeing a given process to be geometrically ergodic. Sufficient condition for transience is also given.

• 대한수학회지
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• 제37권4호
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• pp.503-519
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• 2000

It is well-known that an analytic generic CR submainfold M of codimension m in Cn+m is locally transformed by a biholomorphic mapping to a plane Cn$\times$Rm ⊂ Cn$\times$Cm whenever the Levi form L on M vanishes identically. We obtain such a normalizing biholomorphic mapping of M in terms of the defining function of M. Then it is verified without Frobenius theorem that M is locally foliated into complex manifolds of dimension n.

• 대한수학회보
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• 제37권2호
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• pp.255-263
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• 2000

Let ${X_{nk}}, u_n\; \leq \;k \leq \;u_n,\; n\; \geq\; 1}$ be an array of rowwise independent, but not necessarily identically distributed, random variables with $EX_{nk}$=0 for all k and n. In this paper, we povide a domination condition under which ${\sum^{u_n}}_=u_n\; S_{nk}/n^{1/p},\; 1\; \leq\; p\;<2$ converges completely to zero.

• 대한수학회보
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• 제49권3호
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• pp.495-510
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• 2012

Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

• 대한수학회보
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• 제53권5호
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• pp.1549-1566
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• 2016

Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.

• 품질경영학회지
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• 제7권2호
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• pp.7-10
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• 1979

In this paper the Rao-Blackwell and Lehmann-$Scheff{\acute{e}}$ Theorem are used to drive the minimum variance unbiased estimators of system reliability for a number of distributions when a system consists of n Components whose random life times are assumed to be independent and identically distributed. For the case of a negative exponential life time, we obtain the maximum likelihood estimator of the system reliability and compair it with minimum variance unbiased estimator of the system reliability.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.347-349
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• 1995

In this paper a central limit theorem on $L^P(R)$ for $1{\leq}p<{\infty}$ is obtained with an example when ${X_n}$ is a sequence of independent, identically distributed random variables on $L^P(R)$.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.291-296
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• 2000

Petrov(1996) examined the connection between general moment conditions and the applicability of the strong law lf large numbers to a sequence of pairwise independnt and identically distributed random variables. In this note wee generalize Theorem 1 of Petrov(1996) and also show that still holds under assumption of pairwise negative quadrant dependence(NQD).

• Journal of the Korean Statistical Society
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• 제34권1호
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• pp.11-20
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• 2005

The distributional properties of R = X/(X + Y) and related estimation procedures are derived when X and Y are independent and identically distributed according to the Weibull or Levy distribution. The work is of interest in biological and physical sciences, econometrics, engineering and ranking and selection.