• 대한수학회논문집
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• 제18권1호
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• pp.127-131
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• 2003

Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$\mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $\geq$ 2} with u(1)=1. Then F(x) = 1-x$^{\theta}$, x > 1, ${\theta}$ < -1 if and only if (${\theta}$+1)E[X$_{u(n+1)}$$\mid$X$_{u(m)}$=y] = ${\theta}E[X_{u(n)}$\mid$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\mid$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\mid$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\mid$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\mid$X_{u(m)}=y], n $\geq$ M+1$.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.437-443
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• 2008

In this paper, we establish detailed characterizations of the Weibull distribution by the independence of the upper record values. We prove that X $\in$ W EI($\alpha$), if and only if $\frac{X_{U(n)}}{X_{U(n+1)}+X_{U(n)}}$ and $X_{U(n+1)}$ are independent for n $\geq$ 1. And we show that X $\in$ W EI($\alpha$), if and only if $\frac{X_{U(n+1)}-X_{U(n)}}{X_{U(n+1)}+X_{U(n)}}$ and $X_{U(n+1)}$ are independent for n $\geq$ 1.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.272-277
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• 2001

In order to evaluate variation of fatigue data of the LP steam turbine blade steel, it is important to estimate P - S - N curves to accurately define the probability distributions. In this study, new procedure is introduced to determine the expression of P - S - N curves. For this purpose, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue life were examined by the proposed analysis. Furthermore, parameter estimation for P - S - N curves was performed using various optimization to maximize the correlation coefficient. As a result of this, sequential linear programing method is used for estimation of P - S - N curves.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.229-235
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• 2001

Let {X$\_$n/, n$\geq$1] be a stationary sequence of negatively associated random variables with distribution function F(x)=P(X$_1$$\leq$x). The empirical distribution function F$\_$n/(x) based on X$_1$, X$_2$,....., X$\_$n/ is proposed as an estimator for F$\_$n/(x). Strong consistency and asymptotic normality of F$\_$n/(x) are studied. We also apply these ideas to estimation of the survival function.

• 약학회지
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• 제18권3호
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• pp.183-189
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• 1974

Distribution coefficients between nitrobanzene solution and deionized water, show a straight line when the number of alkyl radicals against the logarithm of distribution coefficient of the salts was plotted. After extracting salts of the indicator and the cationic surfactants with organic solvents, and employing the colorimetric method was used. A calculation method of distribution coefficients of the salts in the organic solvent has been suggested and it could be used for the extraction equilibrium of the primary amine, $CH_{3}(CH_2)_{n}NH_3^+$ secondary amine, $CH_{3}(CH_2)_{n}NH_{2}(CH_3)^+$, tertiary amine $CH_{3}(CH_2)_{n}NH(CH_3)_2^+$ and quaternary ammonium, $CH_{3}(CH_2)_{n}N(CH_3)_3^+$MO$^-$salts, (n=3,5,7,11).

• 대한수학회논문집
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• 제16권2호
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• pp.287-290
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• 2001

Let X$_1$, X$_2$, … be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X(sub)j is an upper record value of this sequence if X(sub)j > max {X$_1$, X$_2$, …, X(sub)j-1}. We define u(n) = min {j│j > u(n-1), X(sub)j > X(sub)u(n-1), n $\geq$ 2} with u(1) = 1. Then F(x) = 1 - e(sup)-x/c, x > 0 if and only if E[X(sub)n(n+1) - X(sub)u(n)│X(sub)u(m) = y] = c or E[X(sub)u(n+2) - X(sub)u(n)│X(sub)u(m) = y] = 2c, n $\geq$ m+1.

• 충청수학회지
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• 제20권1호
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• pp.51-57
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• 2007

In this paper, we establish characterizations of the Pareto distribution by the independence of record values. We prove that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}-X_{U(n+1)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$. And we show that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}-X_{U(n+1)}}{X_{U(n)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.563-572
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• 2008

In this paper, we discuss about a generalization of the Key Distribution Pattern which was proposed by C. Mitchell and F. Piper[6]. It is allowing secure communication between every n-pair of users($n\leq2$) in a large network for reducing storage requirements. We further suggest a generalization of K. Quinn's bounds in [9] for the number of subkeys in such general Key Distribution Patterns.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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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.

• 대한수학회논문집
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• 제17권3호
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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.