• 제목/요약/키워드: Beta function in n variables

검색결과 12건 처리시간 0.171초

ON THE STABILITY OF FUNCTIONAL EQUATIONS IN n-VARIABLES AND ITS APPLICATIONS

  • KIM, GWANG-HUI
    • 대한수학회논문집
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    • 제20권2호
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    • pp.321-338
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    • 2005
  • In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$, where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.

CHARACTERIZATIONS OF BETA DISTRIBUTION OF THE FIRST KIND BY CONDITIONAL EXPECTATIONS OF RECORD VALUES

  • Lee, Min-Young;Chang, Se-Kyung
    • Journal of applied mathematics & informatics
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    • 제13권1_2호
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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.

Sequential confidence intervals for the mean with $\beta$-protection in a certain parameter space

  • Kim, Sung-Lai
    • Journal of the Korean Statistical Society
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    • 제19권2호
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    • pp.113-121
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    • 1990
  • Let ${X_n : n=1,2,\cdots}$ be iid random variables with distribution $P_{\theta}, \theta \in H$ where $H$ is some abstract parameter space. We consider a sequential confidence interval I for the mean $\mu = \mu(\theta)$ of $P_{\theta}$ satisfying $P_{\theta}(\mu \in I) \geq 1-\alpha$ and $P_{\theta}(\mu-\delta(\mu) \in I) \leq \beta$ for all $\theta \in H$ for any given an imprecision real valued function $\delta(\mu) > 0$ and error probabilities $0 < \alpha, \beta < 1$. A one-sided sequential confidence interval is constructed under some restriction of the family {P_{\theta} : \theta \in H}$ and the imprecision function $\delta$. This is extended to the two-sided cases.

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RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF THE PARETO DISTRIBUTION BY RECORD VALUES

  • Lee, Min-Young;Chang, Se-Kyung
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제11권1호
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    • pp.97-102
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    • 2004
  • In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let {$X_n,n\qeq1$}be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F($chi$) and probability density function(pdf) f($chi$). Let $Y_n\;=\;mas{X_1,X_2,...,X_n}$ for $ngeq1$. We say $X_{j}$ is an upper record value of {$X_{n},n\geq1$}, if $Y_{j}$$Y_{j-1}$,j>1. The indices at which the upper record values occur are given by the record times ${u( n)}n,\geq1$, where u(n) = min{j|j >u(n-l), $X_{j}$$X_{u(n-1)}$,n\qeq2$ and u(l) = 1. Suppose $X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$ then E$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$ E$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$ - $\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$ and E$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$ = $\frac{1}{(r+1)\beta}$ [E$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$ - E$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$ - (r+1)E$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$]

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Asymptotic Properties of the Stopping Times in a Certain Sequential Procedure

  • Kim, Sung-Lai
    • Journal of the Korean Statistical Society
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    • 제24권2호
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    • pp.337-347
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    • 1995
  • In the problem of some sequential estimation, the stopping times may be written in the form $N(c) = inf{n \geq n_0; n \geq c^2 S^2_n/\delta^2 (\bar{X}_n)}$ where ${s^2_n}$ and ${\bar{X}_n}$ are the sequences of sample variance and sample mean of the independently and identically distributed (i.i.d.) random variables with distribution $F_{\theta}(x), \theta \in \Theta$, respectively, and $\delta$ is either constant or any given positive real valued function. We obtain some asymptotic normality and asymptotic expectation of the N(c) in various limiting situations. Specially, uniform asymptotic normality and uniform asymptotic expectation of the N(c) are given.

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수도(水稻) 적정시비량(適正施肥量) 결정(決定)에 대한 대체모형(代替模型) (An Alternative Model for Determining the Optimal Fertilizer Level)

  • 장석환
    • 한국토양비료학회지
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    • 제13권1호
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    • pp.21-32
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    • 1980
  • Linear models, with and without site variables, have been investigated in order to develop an alternative methodology for determining optimal fertilizer levels. The resultant models are : (1) Model I is an ordinary quadratic response function formed by combining the simple response function estimated at each site in block diagonal form, and has parameters [${\gamma}^{(1)}_{m{\ell}}$], for m=1, 2, ${\cdots}$, n sites and degrees of polynomial, ${\ell}$=0, 1, 2. (2) Mode II is a multiple regression model with a set of site variables (including an intercept) repeated for each fertilizer level and the linear and quadratic terms of the fertilizer variables arranged in block diagonal form as in Model I. The parameters are equal to [${\beta}_h\;{\gamma}^{(2)}_{m{\ell}}$] for h=0, 1, 2, ${\cdots}$, k site variable, m=1, 2, ${\cdots}$ and ${\ell}$=1, 2. (3) Model III is a classical response surface model, I. e., a common quadratic polynomial model for the fertilizer variables augmented with site variables and interactions between site variables and the linear fertilizer terms. The parameters are equal to [${\beta}_h\;{\gamma}_{\ell}\;{\theta}_h$], for h=0, 1, ${\cdots}$, k, ${\ell}$=1, 2, and h'=1, 2, ${\cdots}$, k. (4) Model IV has the same basic structure as Mode I, but estimation procedure involves two stages. In stage 1, yields for each fertilizer level are regressed on the site variables and the resulting predicted yields for each site are then regressed on the fertilizer variables in stage 2. Each model has been evaluated under the assumption that Model III is the postulated true response function. Under this assumption, Models I, II and IV give biased estimators of the linear fertilizer response parameter which depend on the interaction between site variables and applied fertilizer variables. When the interaction is significant, Model III is the most efficient for calculation of optimal fertilizer level. It has been found that Model IV is always more efficient than Models I and II, with efficiency depending on the magnitude of ${\lambda}m$, the mth diagonal element of X (X' X)' X' where X is the site variable matrix. When the site variable by linear fertilizer interaction parameters are zero or when the estimated interactions are not important, it is demonstrated that Model IV can be a reasonable alternative model for calculation of optimal fertilizer level. The efficiencies of the models are compared us ing data from 256 fertilizer trials on rice conducted in Korea. Although Model III is usually preferred, the empirical results from the data analysis support the feasibility of using Model IV in practice when the estimated interaction term between measured soil organic matter and applied nitrogen is not important.

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소아 신장질환에서 요 β2-microglobulin검사의 분석 (Analysis of urine β2-microglobulin in pediatric renal disease)

  • 김동운;임인석
    • Clinical and Experimental Pediatrics
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    • 제50권4호
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    • pp.369-375
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    • 2007
  • 목 적 : 각 소아 신장 질환에서 요 ${\beta}_2$-M 검사 결과를 비교해 보고, 일차성 신증후군에서 ${\beta}_2$-M 수치와 스테로이드를 사용한 기간과의 상관관계를 확인하고, 신세뇨관 손상을 반영하는 요 ${\beta}_2$-M과 신기능의 보편적 지표인 BUN, Ccr을 비교하여 신기능의 지표로 ${\beta}_2$-M이 유용한 지를 보았다. 방 법 : 2003년 1월부터 2006년 1월까지 중앙대학교 용산병원에 내원하여 24시간 소변검사를 시행 받고 ${\beta}_2$-M 검사를 시행 받은 혈뇨, 부종, 단백뇨 등의 증상이 있는 0-4세 사이의 환아 102명의 신장질환자와 같은 연령대의 대조군 22명을 대상으로 하여 후향적인 자료분석을 하였다. 각 신장 질환을 구분하여 독립변수로 삼았다. 각 신장 질환의 요 ${\beta}_2$-M 검사치를 종속변수로 삼아 독립표본 T검정을 이용하여 통계적 차이를 검증하였다. 또한 일차성 신증후군에서 ${\beta}_2$-M 수치가 의미 있게 높았던 군(양성)과 낮은 군을 구분하여(기준=$150{\mu}g/g-Cr$), 소변에서 단백뇨가 호전되어 퇴원하기까지의 치료기간을 비교하였다. 결 과 : 신장 질환자 102명 중 신증후군이 52명(MCNS(n=45, $72{\pm}45{\mu}g/g-Cr$), MPGN(n=3, $154{\pm}415{\mu}g/g-Cr$), FSGS(n=4, 1$188{\pm}046{\mu}g/g-Cr$), APSGN은 6명($93{\pm}404{\mu}g/g-Cr$), IgA 신병증은 7명($3414{\pm}106{\mu}g/g-Cr$), 급성 신우신염은 9명($742{\pm}160{\mu}g/g-Cr$), 방광염은 16명($179{\pm}168{\mu}g/g-Cr$), 그리고 HSPN은 12명($109{\pm}898{\mu}g/g-Cr$)으로 신증후군 환자가 65%로 가장 많았다. 그 중 IgA 신병증 과 급성 신우신염이 다른 군과 비교하여 24시간 요 ${\beta}_2$-M이 유의하게 높았다(P<0.05). 일차성 신증후군환자의 ${\beta}_2$-M 검사상 높은 군이 낮은 군과 비교하여 유의하게 치료기간이 길었으나(P<0.05), 각 신장질환에서 신기능 지표인 Ccr과 BUN, Cr 등은 24시간 요 ${\beta}_2$-M 과 유의한 차이가 없었다(P>0.05). 결 론 : 각 신장 질환의 24시간 요 ${\beta}_2$-M 수치를 조사한 결과 IgA nephropathy와 급성신우염이 다른 신질환 군과 비교하여 24시간 요 ${\beta}_2$-M 값이 유의하게 높았다. ${\beta}_2$-M 수치는 전반적인 신기능의 지표와 조직병리소견의 예측인자로써는 부적합하나, 상부 하부 요로감염의 감별과 신증후군 환자의 치료기간을 예측하는 데는 유용해 보였다.

남성 만성폐쇄성폐질환자의 삶의 질 관련요인 (Related Factors of Quality of Life in Male Patients with Chronic Obstructive Pulmonary Disease)

  • 이해정;지영주
    • 성인간호학회지
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    • 제23권4호
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    • pp.309-320
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    • 2011
  • Purpose: The purpose of the study was to examine the related factors of quality of life (QOL) among patients with Chronic Obstructive Pulmonary Disease (COPD). Methods: Patients diagnosed with COPD (N=230) were recruited from four hospitals in Kyeong-Nam province, from March 2 to November 30, 2010. The data collection instruments were the Short Form 36, perceived dyspnea measure by Modified Medical Research Council, COPD and Asthma Sleep Impact Scale, COPD Self-efficacy Scale, and Center for Epidemiologic Studies Depression Scale were used. Following the completion of the data collection instruments Pulmonary function was tested. Data were analyzed with descriptive statistics, Pearson correlation and simultaneous multiple regression using SPSS/WIN. Results: The mean QOL of this study was 68.24. Using a multivariate approach, the significant correlates of QOL were depression (${\beta}$=-.37), dyspnea (${\beta}$=-.28), self-efficacy (${\beta}$=.20), and a sufficient degree of household income (${\beta}$=.16). These variables explained 49% of variance in QOL. Conclusion: The study suggests that psychological aspects are an important factor in explaining QOL of the patients. Screening and minimizing depression could be effective strategies in enhancing QOL of patients with COPD and further investigation to reduce depression could warrant the improvement of QOL in patients with COPD.

A Kernel-function-based Approach to Sequential Estimation with $\beta$-protection of Quantiles

  • 김성래;김성균
    • 한국전산응용수학회:학술대회논문집
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    • 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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    • pp.14-14
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    • 2003
  • Given a sequence { $X_{n}$} of independent and identically distributed random variables with F, a sequential procedure for the p-th quantile ξ$_{P}$= $F^{-1}$ (P), 0$\beta$-protection. Some asymptotic properties for the proposed procedure and of an involved stopping time are proved: asymptotic consistency, asymptotic efficiency and asymptotic normality. From one of the results an effect of smoothing based on kernel functions is discussed. The results are also extended to the contaminated case.e.e.

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