• 한국정보디스플레이학회:학술대회논문집
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• 2009.10a
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• pp.1158-1159
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• 2009

Tri-stimulus values of CIE-XYZ and RGB values obtained by photographic film, CCD camera or scanner depend on the spectral sensitivity of imaging devices and the spectral radiant distribution of the illumination. It is important to record and reproduce the reflectance spectra of the object for true device independent color reproduction and high accurate recording of the scene. In this paper, a method to record the reflection spectra of the object is introduced and its application to spectral endoscopes is presented.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.541-550
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• 2007

This paper presents characterizations of the power distribution with the parameter $\beta=1$ by the independence of the lower record values. We prove $X\;{\in}\;POW({\alpha},\;1)$ for ${\alpha}\;>\;0$, if and only if $\frac{X_{L(n)}}{X_{L(m)}}$ and $X_{L(m)}$ for $1\;{\leq}\;m\;<\;n$ are independent. And we prove that $X\;{\in}\;POW({\alpha},\;1)$ for ${\alpha}\;>\;0$, if and only if $\frac{X_{L(m)}-X_{L(m+1)}}{X_{L(m)}}$ and $X_{L(m)$ for $m\;{\geq}\;1$ are independent or $\frac{X_{L(m)}-X_{L(m+1)}}{X_{L(m+1)}}$ and $X_{L(m)}$ for $m\;{\geq}\;1$ are independent.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.139-146
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• 2007

In this paper, we present characterizations of the power function distribution by the independence of record values. We establish that $X{\in}$ POW(1, ${\nu}$) for ${\nu}$ > 0, if and only if $\frac{X_{L(n)}}{X_{L(n)}-X_{L(n+1)}}$ and $X_{L(n)}$ are independent for $n{\geq}1$. And we prove that $X{\in}$ POW(1, ${\nu}$) for ${\nu}$ > 0; if and only if $\frac{X_{L(n+1)}}{X_{L(n)}-X_{L(n+1)}}$ and $X_{L(n)}$ are independent for $n{\geq}1$. Also we characterize that $X{\in}$ POW(1, ${\nu}$) for ${\nu}$ > 0, if and only if $\frac{X_{L(n)}+X_{L(n+1)}}{X_{L(n)}-X_{L(n+1)}}$ and $X_{L(n)}$ are independent for $n{\geq}1$.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.375-381
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• 2006

This paper presents characterizations based on the identical distribution and the finite moments of the exponential distribution by record values. We prove that $X{\in}EXP({\sigma})$, ${\sigma}$>0, if and only if $X_{U(n+k)}-X_{U(n)}$ and $X_{U(n)}-X_{U(n-k)}$ for n > 1 and $k{\geq}1$ are identically distributed. Also, we show that $X{\in}EXP({\sigma})$, ${\sigma}$>0, if and only if $E(X_{U(n+k)}-X_{U(n)})=E(X_{U(n)}-X_{U(n-k)})$ for n>1 and $k{\geq}1$.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.955-961
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• 2009

In this paper, we establish some characterizations which is satisfied by the independence of the upper record values from the Pareto distribution. We prove that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$, $1\;{\le}\;m\;<\;n$ are independent. We show that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0 if and only if $\frac{X_{U(n)}+X_{U{(n+1)}}}{X_{U(n)}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent. And we characterize that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}+X_{U{(n+1)}}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.405-416
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• 2013

This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.279-285
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• 2008

This paper presents some characterizations of the Weibull distribution by the independence of record values. We prove that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. We show that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. And we establish that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}+X_{U(n)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.471-477
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• 2007

In this paper we establish some recurrence relations satisfied by the quotient moments of the upper record values from the Weibull distribution. Suppose $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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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 $n{\geq}1$.

• Communications for Statistical Applications and Methods
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• v.30 no.5
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• pp.453-465
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• 2023

The prediction problem of univariate records, though not addressed in multivariate records, has been discussed by many authors based on records values. There are various definitions for multivariate records among which depth-based records have been selected for the aim of this paper. In this paper, by means of the maximum likelihood and conditional median methods, point and interval predictions of depth values which are related to the future depth-based multivariate records are considered on the basis of the observed ones. The observations derived from some elements of the elliptical distributions are the main reason of studying this problem. Finally, the satisfactory performance of the prediction methods is illustrated via some simulation studies and a real dataset about Kermanshah city drought.