• Title/Summary/Keyword: 포아송의 혼합분포

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The Reanalysis of the Donation Data Using the Zero-Inflated Possion Regression (0이 팽창된 포아송 회귀모형을 이용한 기부회수 자료의 재분석)

  • Kim, In-Young;Park, Tae-Kyu;Kim, Byung-Soo
    • The Korean Journal of Applied Statistics
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    • v.22 no.4
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    • pp.819-827
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    • 2009
  • Kim et al. (2006) analyzed the donation data surveyed by Voluneteer 21 in year 2002 at South Korea using a Poisson regression based on the mixture of two Poissons and detected significant variables for affecting the number of donations. However, noting the large deviation between the predicted and the actual frequencies of zero, we developed in this note a Poisson regression model based on a distribution in which zero inflated Poisson was added to the mixture of two Poissons. Thus the population distribution is now a mixture of three Poissons in which one component is concentrated on zero mass. We used the EM algorithm for estimating the regression parameters and detected the same variables with Kim et al's for significantly affecting the response. However, we could estimate the proportion of the fixed zero group to be 0.201, which was the characteristic of this model. We also noted that among two significant variables, the income and the volunteer experience(yes, no), the second variable could be utilized as a strategric variable for promoting the donation.

Moments of the Bivariate Zero-Inflated Poisson Distributions (이변량 영과잉-포아송 분포의 적률)

  • Kim, Kyung-Moo;Lee, Sung-Ho;Kim, Jong-Tae
    • Journal of the Korean Data and Information Science Society
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    • v.9 no.1
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    • pp.47-56
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    • 1998
  • Zero-Inflated Poisson models are mixed models of the Poisson and Bernoulli models. Recently Zero-Inflated Poisson distributions have been used frequently rather than previous Poisson distributions because the developement of industrial technology make few defects in manufacturing process. It is important that univariate Zero-Inflated Poisson distributions are extended to bivariate distributions to generalize the multivariate distributions. In this paper we proposed three types of the bivariate Zero-Inflated Poisson distributions and obtained these moments. We compared the three types of distributions by using the moments.

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The Analysis of the Number of Donations Based on a Mixture of Poisson Regression Model (포아송 분포의 혼합모형을 이용한 기부 횟수 자료 분석)

  • Kim In-Young;Park Su-Bum;Kim Byung-Soo;Park Tae-Kyu
    • The Korean Journal of Applied Statistics
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    • v.19 no.1
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    • pp.1-12
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    • 2006
  • The aim of this study is to analyse a survey data on the number of charitable donations using a mixture of two Poisson regression models. The survey was conducted in 2002 by Volunteer 21, an nonprofit organization, based on Koreans, who were older than 20. The mixture of two Poisson distributions is used to model the number of donations based on the empirical distribution of the data. The mixture of two Poisson distributions implies the whole population is subdivided into two groups, one with lesser number of donations and the other with larger number of donations. We fit the mixture of Poisson regression models on the number of donations to identify significant covariates. The expectation-maximization algorithm is employed to estimate the parameters. We computed 95% bootstrap confidence interval based on bias-corrected and accelerated method and used then for selecting significant explanatory variables. As a result, the income variable with four categories and the volunteering variable (1: experience of volunteering, 0: otherwise) turned out to be significant with the positive regression coefficients both in the lesser and the larger donation groups. However, the regression coefficients in the lesser donation group were larger than those in larger donation group.

On the Extension of Test Statistics for Detecting Negative Binomial Departures from the Poisson Assumption (포아송으로부터 부의 이항분포로의 이탈에 대한 검정통계량의 확장)

  • 이선호
    • Journal of the Korean Statistical Society
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    • v.22 no.2
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    • pp.171-190
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    • 1993
  • 포아송분포로부터 부의 이항분포로의 이탈을 검색하는 통계량들이 자료의 형태에 따라 여러가지 제시되었다. 그런데 대립가설인 부의 이항분포의 모수화 방법에 따라 분산과 평균의 구조가 변하고 국소 최적 검정 통계량도 달라진다는 것이 알려졌다. 본 논문에서는 대립가설을 일반적인 포아송 혼합분포로까지 확장시키고, 일반적인 형태의 분산과 평균의 구조에도 검정 가능한 새로운 통계량 L을 소개하고 있다. 또한 L 통계량은 포아송 분포로부터 부의 이항분포로의 이탈을 다루는 기존의 여러 통계량들의 일반화된 형태임을 보였다. 점근적 상대효율과 모의 실험을 통하여 L 통계량과 기존의 통계량들을 비교한 결과 분산과 평균사이의 구조에 상관없이 L 통계량이 우수한 것임을 입증하였다.

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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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    • v.8 no.1
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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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Infinite Failure NHPP Software Mixture Reliability Growth Model Base on Record Value Statistics (기록값 통계량에 기초한 무한고장 NHPP 소프트웨어 혼합 신뢰성장 모형에 관한 연구)

  • Kim, Hee-Cheul;Shin, Hyun-Cheul;Kim, Kyung-Soo
    • Convergence Security Journal
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    • v.7 no.3
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    • pp.51-60
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    • 2007
  • Infinite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, exponential distribution and Rayleigh distribution model was reviewed, proposes the mixture reliability model, which made out efficiency substituted for situation for failure time Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE and Kolmogorov distance, for the sake of efficient model, was employed. Analysis of failure using S27 data set for the sake of proposing shape parameter of the mixture distribution was employed. This analysis of failure data compared with the mixture distribution model and the existing model(using arithmetic and Laplace trend tests, bias tests) is presented.

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Estimation in Mixture of Shifted Poisson Distributions

  • Oh, Chang-Hyuck
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.4
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    • pp.1209-1217
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    • 2006
  • For the mixture of shifted Poisson distributions, a method of parameter estimation is proposed. The range of the shifted parameters are estimated first and for each shifted parameter set EM algorithm is applied to estimate the other parameters of the distribution. Among the estimated parameter sets, one with minimum likelihood for given data is to be set as the final estimate. In simulation experiments, the suggested estimation method shows to have a good performance.

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Estimation in Mixture of Shifted Poisson Distributions with Known Shift Parameters

  • Lee, Hyun-Jung;Oh, Chang-Hyuck
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.3
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    • pp.785-794
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    • 2006
  • Suggested is an EM algorithm for estimation in mixture of shifted Poisson distributions with known shift parameters. For this type of mixture distribution, we have to utilize values of shift parameters to determine whether each of data belongs to some component distribution. We propose a method of estimating values of component information and then follow typical EM methodology. Simulation results show that the algorithm provides reasonable performance for the distribution.

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A Study on the Performance Analysis of Broadband ISDN Traffic (광대역 ISDN의 트래픽 성능분석에 관한 연구)

  • 구창회;박광채;이재호
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.18 no.7
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    • pp.980-988
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    • 1993
  • In this paper, performance of 8-ISDN traffic for the buffer size which is requested of important parameters in switch/multiplexer of B-ISDN with multimedia traffic is analyzed. Multimedia traffic is modeled as a traffic, which is composed of poisson distribution traffic and burst traffic with exponential/geometric ON time duration(Burst duration) Performance of traffic which is modeled as a multimedia traffic is analysed and buffer size, can provide the high quality service, is presented for the cell loss probability. It is simulated using event scheduling approach method which is provided by simulation package, PC SIMSCRIPT II.5. Simulation program is composed of PREAMBLE, MAIN, INITIAL, ARRIVAL, DEPARTURE and STOP·SIM modules. Specially, in case of mixed traffic simulation, ARRIVAL module is composed of ARRIVAL I and ARRIVAL II, and cells are generated independently by each module.

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Mixed-effects zero-inflated Poisson regression for analyzing the spread of COVID-19 in Daejeon (혼합효과 영과잉 포아송 회귀모형을 이용한 대전광역시 코로나 발생 동향 분석)

  • Kim, Gwanghee;Lee, Eunjee
    • The Korean Journal of Applied Statistics
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    • v.34 no.3
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    • pp.375-388
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    • 2021
  • This paper aims to help prevent the spread of COVID-19 by analyzing confirmed cases of COVID-19 in Daejeon. A high volume of visitors, downtown areas, and psychological fatigue with prolonged social distancing were considered as risk factors associated with the spread of COVID-19. We considered the weekly confirmed cases in each administrative district as a response variable. Explanatory variables were the number of passengers getting off at a bus station in each administrative district and the elapsed time since the Korean government had imposed distancing in daily life. We employed a mixed-effects zero-inflated Poisson regression model because the number of cases was repeatedly measured with excess zero-count data. We conducted k-means clustering to identify three groups of administrative districts having different characteristics in terms of the number of bars, the population size, and the distance to the closest college. Considering that the number of confirmed cases might vary depending on districts' characteristics, the clustering information was incorporated as a categorical explanatory variable. We found that Covid-19 was more prevalent as population size increased and a district is downtown. As the number of passengers getting off at a downtown district increased, the confirmed cases significantly increased.