• 제목/요약/키워드: N-values

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ON CHARACTERIZATIONS OF THE POWER DISTRIBUTION VIA THE IDENTICAL HAZARD RATE OF LOWER RECORD VALUES

  • Lee, Min-Young
    • 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 $V=X_{L(n+2)}/X_{L(n+1)}$.

CHARACTERIZATIONS OF THE LOMAX, EXPONENTIAL AND PARETO DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF RECORD VALUES

  • Lee, Min-Young;Lim, Eun-Hyuk
    • 충청수학회지
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    • 제22권2호
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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.

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ON CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENT PROPERTY OF RECORD VALUES

  • Lee, Min-Young;Lim, Eun-Hyuk
    • 충청수학회지
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    • 제23권2호
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    • pp.245-250
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    • 2010
  • We present characterizations of the Weibull distribution by the independent property of record values that F(x) has a Weibull distribution if and only if $\frac{X_{U(m)}}{X_{U(n)}}$ and $X_{U(n)}$ or $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(n)}$ are independent for $1{\leq}m.

CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENCE OF THE UPPER RECORD VALUES

  • Chang, Se-Kyung;Lee, Min-Young
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제15권2호
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    • pp.163-167
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    • 2008
  • This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that $X\;{\in}\;W\;EI ({\alpha})$, if and only if $\frac {X_{U(n+l)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent or $\frac {X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. And also we establish 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 $X_{U(n+1)}$ for $n{\geq}1$ are independent.

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Determining N value from SPT blows for 30 cm penetration in weathered strata

  • Sun, Chang-Guk;Cho, Hyung-Ik;Kim, Han-Saem;Lee, Moon-Gyo
    • Geomechanics and Engineering
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    • 제28권6호
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    • pp.625-636
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    • 2022
  • The standard penetration test (SPT) obtaining the N value of the number of blows has been widely used in various subsurface conditions, including in weathered soil and rock on fresh bedrock, in geotechnical studies pertaining to the design of foundations and earth structures. This study examined the applicability of SPTs terminated conventionally after 50 blows for a penetration of less than 30 cm, particularly in weathered strata, at four sites in Korea. The N values obtained during practical SPTs are typically extrapolated linearly at 30 cm penetration, despite the possibility of a nonlinear relationship between blow counts and penetration. Such nonlinearity in weathered strata has been verified by performing special SPTs ensuring 30 cm penetration. To quantify the nonlinearity in dense strata, we conducted statistical regression analyses comparing the differences (DN) between the N values measured by the special SPTs and those extrapolated using the practical approach with the differences (DP) between the 30 cm penetration and the penetration during 50 blows. Bi-linear relationship models between DN and DP were subsequently proposed for determining the N values at 30 cm penetration in weathered strata. The N values reflecting nonlinearity could be determined from the linearly extrapolated N values by adding a modeled DN value.

경산시 지하수의 수질특성에 관한 연구 (A Study on the Characteristics of Groundwaters in Gyeongsan City)

  • 송성숙;박병윤;이부용
    • 한국환경과학회지
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    • 제16권6호
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    • pp.677-682
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    • 2007
  • This study was performed to provide the basic information on characteristics of groundwater pollution in Gyeongsan city. Forty two groundwater samples were collected, and pH, DO, COD, $NH_3-N,\;NO_3^--N$, T-N, $PO_4^{3-}-P$, Cl, Ca, Mg, hardness, evaporate residues and others were investigated. And, ANOVA analyses were carried out to reveal the differences in water pollution indicator values of by industry, commerce/residence and agriculture areas. The results were as follows. 1. The mean values of pH, DO, COD, $NH_3-N,\;NO_3^--N$, T-N, $PO_4^{3-}-P$, Cl, evaporate residues, Ca and hardness were 6.9, $7.9mg/\ell,\;0.4mg/\ell,\;2.44mg/\ell,\;2.73mg/\ell,\;6.06mg/\ell,\;0.82mg/\ell,\;32.72mg/\ell,\;381.67mg/\ell,\;41.53mg/\ell,\;177.17mg/\ell$, respectively. 2. As groundwater became deeper, the values of Cl, Ca, Mg, Na, hardness and evaporate residues remarkably increased, but those of COD, $NH_3^--N,\;NO_3^--N,\;NO_2^-N$, T-N decreased. 3. The values of COD, Cl, Ca, Mg, Na, hardness and evaporate residues were very high in industrial area, and those of $NH_3-N,\;NO_2^--N$, T-N were very high in commercial/residential area, and those of $NO_3^--N$ were a little high in agricultural area. 4. The correlations between depth and each value of Mg, Na, Fe, hardness and evaporate residues were highly positive, and those between DO and each value of Mg, Cu, Fe, hardness and evaporate residues were highly negative. 5. According to ANOVA analyses, the differences in three area groups (industry, commerce/residence and agriculture) on the values of $NH_3-N$, T-N, evaporate residues, hardness, Ca, Mg, K and Fe were significant at 1% level.

ON CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE UPPER RECORD VALUES

  • Chang, Se-Kyung;Lee, Min-Young;Park, Young-Seo
    • 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.

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요소와 돈분퇴비 시용에 따른 포트 재배 옥수수의 질소동위원소 자연존재비 차이 (Natural 15N Abundances of Corn Treated with Urea and Composted Pig Manure in a Pot Experiment)

  • 최우정;이상모;김경철;김판건;류지혁;류순호
    • 한국토양비료학회지
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    • 제34권4호
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    • pp.284-291
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    • 2001
  • 유기질비료와 화학비료 시용에 따른 작물체의 질소동위원소비 (${\delta}^{15}N$) 차이 유무를 조사하기 위해 포트 조건에서 돈분 퇴비 (+13.9‰) 와 요소(-2.3‰) 를 시용하여 70일간 재배한 옥수수의 뿌리, 줄기, 잎, 알곡에 대한 ${\delta}^{15}N$ 값을 분석하였고, 동위원소 질량수지 방정식을 이용하여 옥수수 전부위에 대한 ${\delta}^{15}N$ 값을 계산하였다. 옥수수의 ${\delta}^{15}N$값은 토양 질소의 영향과 질소의 형태변환과정에 수반되는 동위원소분할효과에 의해 시용한 퇴비와 요소의 ${\delta}^{15}N$ 값과 차이를 보였다. 옥수수 전부위, 뿌리 및 줄기의 ${\delta}^{15}N$ 값은 요소와 퇴비 시용에 따른 유의성 있는 차이 (p<0.05)를 나타내지 않았지만, 잎과 알곡의 ${\delta}^{15}N$ 값은 각각 퇴비 처리구(+14.3‰, +16.2‰) > 무처리구(+13.2‰, +13.9‰) > 요소-퇴비 혼합처리구(+10.1‰, +12.6‰) 요소 처리구 (+10.1‰, +12.4‰)의 순서로 유의성 있는 차이가 나타났다. 따라서, 본 연구는 시용 질소원의 종류(퇴비 또는 화학비료)를 확인하는데 있어서 작물의 잎 또는 알곡의 ${\delta}^{15}N$ 값 활용 가능성을 제시해주는 것으로 판단되었다. 하지만, 보다 일반적인 결론을 얻기 위해서는 다양한 종류의 토양과 작물에 대한 연구가 요구된다.

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CHARACTERIZATIONS BASED ON THE INDEPENDENCE OF THE EXPONENTIAL AND PARETO DISTRIBUTIONS BY RECORD VALUES

  • LEE MIN-YOUNG;CHANG SE-KYUNG
    • Journal of applied mathematics & informatics
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    • 제18권1_2호
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    • pp.497-503
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    • 2005
  • This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.