• 제목/요약/키워드: 이항분포

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Binomial Sampling Plans for the Citrus Red Mite, Panonychus citri(Acari: Tetranychidae) on Satsuma Mandarin Groves in Jeju (온주밀감에서 귤응애의 이항표본조사법 개발)

  • 송정흡;이창훈;강상훈;김동환;강시용;류기중
    • Korean journal of applied entomology
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    • 제40권3호
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    • pp.197-202
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    • 2001
  • The density of citrus red mite(CRM), Panonychus citri(McGregor), on the commercial satsuma mandarin Citrus unshiu L. groves were determined by counts of the number of CRM per leaf using by leaf sample in Jeju for 2 years. Binomial sampling plans were developed based on the relationship between the mean density per leaf(m) and the proportion of leaf infested with less than T mites per leaf($P_{T}$), according to the empirical model $ln(m)={\alpha}+{\beta}ln(-ln(1-P_{T}))$. T was defined as tally threshold, and set to 1, 3, 5 and 7 mites per leaf in this study. Increasing sample size, regardless of tally threshold, had little effects on the precision of the binomial sampling plan. Increasing sampling size had little effect on the precision of the estimated mean regardless of tally thresholds. T=1 was chosen as the best tally threshold for estimating densities of CRM based on the precision of the model. The binomial model with T=1 provided reliable predictions of mean densities of CRM observed on the commercial satsuma mandarin groves. Binomial sequential sampling procedure were developed for classifying the density of CRM. A binomial sampling program for decision-making CRM population level based on action threshold of 2 mites per leaf was obtained.

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Criterion of discrete unimodal mixtures (이산분포 혼합의 단봉성이 성립하기 위한 조건)

  • 최대우
    • The Korean Journal of Applied Statistics
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    • 제8권1호
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    • pp.159-167
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    • 1995
  • Considering special discrete distribution of exponential family as a sequence with respect to the points of support, the squence is unimodal in some sense. In this paper, we study under what condition the mixture of that discrete distribution with respect to a parameter is unimodal. We derive the maximal interval of the parameter in which each mixture of the discrete distribution such as Binomial and Poisson is always unimodal.

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On the Multivariate Poisson Distribution with Specific Covariance Matrix

  • Kim, Dae-Hak;Jeong, Heong-Chul;Jung, Byoung-Cheol
    • Journal of the Korean Data and Information Science Society
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    • 제17권1호
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    • pp.161-171
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    • 2006
  • In this paper, we consider the random number generation method for multivariate Poisson distribution with specific covariance matrix. Random number generating method for the multivariate Poisson distribution is considered into two part, by first solving the linear equation to determine the univariate Poisson parameter, then convoluting independent univariate Poisson variates with appropriate expectations. We propose a numerical algorithm to solve the linear equation given the specific covariance matrix.

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일반혼합이항모형에서 평가일치도의 로버스트 추정

  • 엄종석
    • Communications for Statistical Applications and Methods
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    • 제2권2호
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    • pp.74-84
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    • 1995
  • 혼합이항모형은 생물학, 혹은 심리학분야에서 많이 다루는 모형이다. 이 혼합모형에서 진단자간의 일치도를 나타내는 k 는 이항모형에 혼합되어지는 사전분포 $\xi$(p)에 따라 다른 형태를 갖는다. 그래서 $\xi$(p)에 의존적이지 않은 모수를 정의 하고, 이에 대한 실증적 추정값 $\hat k$을 일반혼합이항모형에서 k에 대한 추정값으로 사용하였다. 매개모수의 영향을 줄이기 위하여 모수를 직교화하였다. 베타이항모형으로 부터 표본을 추출하여 구한 최우추정값 $\hat k_m$과 이 표본을 이용하여 구한 $\hat k$을 비교하여 본 결과 k와 $\lambda$가 직교하는 영역에서 $\hat k$$\hat k_m$보다 편기가 작아지는 경우가 있을 만큼 $\hat k$이 효과적이었다.

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Estimation of Advertising Exposure Distribution by Zero-inflation Regression Models (영과잉 회귀모형을 이용한 광고노출분포 추정)

  • Lee, Dong-Hee
    • Journal of the Korean Data Analysis Society
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    • 제20권6호
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    • pp.2841-2852
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    • 2018
  • This study examines regression modeling method using zero-inflated distribution in relation to estimation of exposure distribution required in advertisement media planning. Exposure distribution is the percentage of audiences that are exposed each time the ad is repeated. Such an exposure distribution plays a very important role in providing basic information necessary for calculating various indicators for quantitatively measuring the advertising effect. Especially, due to the decrease of advertising price and the spread of various media, the frequency of the advertisement or the broadcasting of specific advertisements has been greatly increased compared to the past. As a result, the frequency of exposure is relatively decreasing. In this situation, the number of individuals who are not exposed to the media, that is, are not exposed to advertising structurally is increasing. This research proposes advertising exposure distribution models using a zero-inflated regression model, and conducts a comparative study using actual cases.

지역별 주택분포와 주거형태의 변화에 관한 고찰

  • Kim, Su-Deok
    • Environmental and Resource Economics Review
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    • 제4권1호
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    • pp.125-154
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    • 1994
  • 인구 및 주택건축 총조사보고서의 년도별로 분류된 잔존주택에 관한 정보에는 멸실되어 소실된 주택과 당시의 신규주택분에 관한 정보를 얻을 수 없고, 센서스이후 추계된 최근의 지역통계는 기간내 발생한 멸실주택에 대한 추계과정이 생략되어 주택의 통계가 과대계상되어 있다. 본 연구는 지역별 주택수 예측의 방법을 제시하고 주택형태별, 평형별, 난방형태별 분포현황의 분석과 전망을 시도하였다. 지역별 주택수의 예측에서 지역별 주택의 건축년도와 멸실이 독립이라는 가정하에 주택의 수명, 최대멸실확율을 보이는 지역별 이항분포(Binomial Distribution)를 찾아내었다. 주어진 Data의 특성에 따라 얻어진, 지역별로 다른 최적의 분포와 이에 따라 산정된 각 시점의 신규주택수를 이용하여 미래의 주택수를 전망하였다. 주택형태, 평형, 난방시설분포의 현황분석과 전망은 각 형태의 비율을 산정, 추정하는 방식을 택했다.

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Asymptotic distribution of estimator in INAR(1) process with negative binomial marginal (주변분포가 음이항 분포를 따르는 INAR(1)모형에서 추정량의 점근분포)

  • 김희영;박유성
    • The Korean Journal of Applied Statistics
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    • 제9권1호
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    • pp.111-124
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    • 1996
  • In this paper, we consider the first-order integer valued autoregressive(INAR(1)) model where correlation structure is similar to that of the continuous valued AR(1) process. Several methods for estimating the parameters of the INAR(1) process with negative binomial marginal are discussed. We derive asymptotic distributions of these estimators. The results of a simulation study for these estimators methods show that the estimator which we present in this paper is better than the estimator which Klimko and Nelson(1978) presented. As an application we considered the estimator of M/M/1 queue length.

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A new sample selection model for overdispersed count data (과대산포 가산자료의 새로운 표본선택모형)

  • Jo, Sung Eun;Zhao, Jun;Kim, Hyoung-Moon
    • The Korean Journal of Applied Statistics
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    • 제31권6호
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    • pp.733-749
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    • 2018
  • Sample selection arises as a result of the partial observability of the outcome of interest in a study. Heckman introduced a sample selection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality. Recently sample selection models for binomial and Poisson response variables have been proposed. Based on the theory of symmetry-modulated distribution, we extend these to a model for overdispersed count data. This type of data with no sample selection is often modeled using negative binomial distribution. Hence we propose a sample selection model for overdispersed count data using the negative binomial distribution. A real data application is employed. Simulation studies reveal that our estimation method based on profile log-likelihood is stable.

Analysis of Weights Given to Observations in the Bayesian Reliability Prediction (베이지안 기법을 이용한 신뢰도 예측 시 관측치에 주어지는 가중치 분석에 관한 연구)

  • Yang, Hee Joong
    • Journal of Korean Society of Industrial and Systems Engineering
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    • 제22권51호
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    • pp.53-61
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    • 1999
  • 평균치에 적용되는 credibility formula를 분산에도 적용하여 응용 할 수 있는 extended credibility formula를 개발한다. 간단한 베이지안 신뢰도 예측모형을 구축하고 이 모형에 extended credibility formula를 적용한다. 감마 사전분포 - 포아송 우도의 경우와 베타 사전분포 - 이항분포 우도의 경우에 대해 extended credibility formula를 적용해 관측치에 주어진 가중치에 따라 사후 분산이 어떻게 변화하는지를 분석한다. 사후분산도 사후평균과 마찬가지로 사전값과 관측값의 가중평균으로 표시될 수 있다는 것을 증명한다. 가중치와 불확실성 감소율간의 관계도 연구된다. 이와 같은 가중치에 따른 사전 및 사후분포의 변화 양식에 대한 이해는 올바른 사전분포를 설정하는데 큰 도움이 될 수 있다.

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A simulation study for the approximate confidence intervals of hypergeometric parameter by using actual coverage probability (실제포함확률을 이용한 초기하분포 모수의 근사신뢰구간 추정에 관한 모의실험 연구)

  • Kim, Dae-Hak
    • Journal of the Korean Data and Information Science Society
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    • 제22권6호
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    • pp.1175-1182
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    • 2011
  • In this paper, properties of exact confidence interval and some approximate confidence intervals of hyper-geometric parameter, that is the probability of success p in the population is discussed. Usually, binomial distribution is a well known discrete distribution with abundant usage. Hypergeometric distribution frequently replaces a binomial distribution when it is desirable to make allowance for the finiteness of the population size. For example, an application of the hypergeometric distribution arises in describing a probability model for the number of children attacked by an infectious disease, when a fixed number of them are exposed to it. Exact confidence interval estimation of hypergeometric parameter is reviewed. We consider the approximation of hypergeometirc distribution to the binomial and normal distribution respectively. Approximate confidence intervals based on these approximation are also adequately discussed. The performance of exact confidence interval estimates and approximate confidence intervals of hypergeometric parameter is compared in terms of actual coverage probability by small sample Monte Carlo simulation.