• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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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 $V=X_{L(n+2)}/X_{L(n+1)}$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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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 $1{\leq}m$ < $n$.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.91-97
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• 2020

Presented in this paper is a characterization of Weibull distribution by an independence property of upper record values that X_k has a Weibull distribution if and only if ${\frac{X_U(m)}{X_U(n)}}$ and X_U(s) are independent for 1 ≤ m < n < s.

• The Transactions of the Korea Information Processing Society
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• v.4 no.2
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• pp.483-490
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• 1997

The evalution of the cumulative distridution function of the noncentral $X^2$ distribution required in approxi-mate determination of the $X^2$ test. Many approximations to the cumulative distribution function of the noncentral $X^2$ distribution have been suggested. However, in selecting an approximations both simplicity and accuracy should be considered. In this note we compared various approximations in terms of accuracy and efficiency.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.3-10
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• 1978

Let $X_i,...,X_n$ be a random sample from a distribution with cumulants $K_1, K_2,...$. The statistic $t = \frac{\sqrt{x}(\bar{X}-K_1)}{S}$ has the well-known 'student' distribution with $\nu = n-1$ degrees of freedom if the $X_i$ are normally distributed (i.e., $K_i = 0$ for $i \geq 3$). An Edgeworth series expansion for the distribution of t when the $X_i$ are not normally distributed is obtained. The form of this expansion is Prob $(t

• Korean Journal of Materials Research
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• v.22 no.8
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• pp.385-389
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• 2012

Significant improvements in the switching voltage distribution are required for the development of unipolar resistive memory devices using $MnO_x$ thin films. The $V_{set}$ of the as-grown $MnO_x$ film ranged from 1 to 6.2 V, whereas the $V_{set}$ of the oxygen-annealed film ranged from 2.3 to 3 V. An excess of oxygen in an $MnO_x$ film leads to an increase in $Mn^{4+}$ content at the $MnO_x$ film surface with a subsequent change in the $Mn^{4+}/Mn^{3+}$ ratio at the surface. This was attributed to the change in $Mn^{4+}/Mn^{3+}$ ratios at the $MnO_x$ surface and to grain growth. Oxygen annealing is a possible solution for improving the switching voltage distribution of $MnO_x$ thin films. In addition, crystalline $MnO_x$ can help stabilize the $V_{set}$ and $V_{reset}$ distribution in memory switching in a Ti/$MnO_x$/Pt structure. The improved uniformity was attributed not only to the change of the crystallinity but also to the redox reaction at the interface between Ti and $MnO_x$.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.245-254
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• 2004

This paper derives a distribution function of the terminal value and running maximum of two-dimensional Brownian motion {X($\tau$) = (X$_1$($\tau$), X$_2$ ($\tau$))', $\tau$ 〉0}. One random variable of the joint distribution is the terminal time value, X$_1$ (T). The other random variable is the maximum of the Brownian motion {X$_2$($\tau$), $\tau$〉} between time s and time t. With this distribution function, this paper also derives an explicit pricing formula for an outside barrier option whose monitoring period starts at an arbitrary date and ends at another arbitrary date before maturity.