• Title/Summary/Keyword: N-values

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

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

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

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

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

  • Lee, Min-Young;Lim, Eun-Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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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
    • The Pure and Applied Mathematics
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    • v.15 no.2
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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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    • v.28 no.6
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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.

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

  • Song, Sung-Sook;Park, Byoung-Yoon;Lee, Bu-Yong
    • Journal of Environmental Science International
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    • v.16 no.6
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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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    • v.26 no.1_2
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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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Natural 15N Abundances of Corn Treated with Urea and Composted Pig Manure in a Pot Experiment (요소와 돈분퇴비 시용에 따른 포트 재배 옥수수의 질소동위원소 자연존재비 차이)

  • Choi, Woo-Jung;Lee, Sang-Mo;Kim, Kyoung-Cheol;Kim, Pan-Gun;Yoo, Ji-Hyeok;Yoo, Sun-Ho
    • Korean Journal of Soil Science and Fertilizer
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    • v.34 no.4
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    • pp.284-291
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    • 2001
  • To study whether N isotope composition (${\delta}^{15}N$) of crop reflects the kind of fertilizer (chemical or organic) applied to field, a pot experiment was conducted. Corn (Zea mays L.) was cultivated under greenhouse conditions for 70 days. Composted pig manure and urea were applied at 0 and 0 (C0U0), at 0 and 300 (COU2), at 300 and 0 (C2U0) and at 150 and $150kg\;N\;ha^{-1}$ (C1U1), respectively. The ${\delta}^{15}N$ values of composted pig manure and urea were + 13.9‰ and -2.3‰, respectively. The ${\delta}^{15}N$ values of whole parts (roots + stems + leaves + grains) were + 12.7, + 12.9, + 14.0 and + 13.0‰ for C0U0, C0U2, C2U0 and C1U1 treatments, and were not significantly affected by the application of isotopically different N sources (P<0.05). However, leaves or grains showed significantly (P<0.05) different ${\delta}^{15}N$ values between treatments. The ${\delta}^{15}N$ values of leaves and grains were + 14.3 and + 16.2‰ for C2U0, +13.2 and +13.9‰ for C0U0, +10.1 and + 12.6‰ for C1U1 and +10.1 and +12.4‰ for C0U2 treatments. The different ${\delta}^{15}N$ values of corn from the values of N sources (compost and urea) applied to soil showed that the ${\delta}^{15}N$ values of corn were affected not only by the isotope composition of N source, but also by N pool mixing and isotope fractionation accompanying N transformation. This study suggests that although the ${\delta}^{15}N$ values of crop are not identical to the ${\delta}^{15}N$ values of N sources applied to fields, the application of isotopically different N sources such as compost and chemical fertilizer may result in qualitative difference in ${\delta}^{15}N$ values of crop.

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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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    • v.18 no.1_2
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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.