• Title/Summary/Keyword: Size-based Poisson Distribution

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ON SIZE-BIASED POISSON DISTRIBUTION AND ITS USE IN ZERO-TRUNCATED CASES

  • Mir, Khurshid Ahmad
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.3
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    • pp.153-160
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    • 2008
  • A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.

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Methods and Sample Size Effect Evaluation for Wafer Level Statistical Bin Limits Determination with Poisson Distributions (포아송 분포를 가정한 Wafer 수준 Statistical Bin Limits 결정방법과 표본크기 효과에 대한 평가)

  • Park, Sung-Min;Kim, Young-Sig
    • IE interfaces
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    • v.17 no.1
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    • pp.1-12
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    • 2004
  • In a modern semiconductor device manufacturing industry, statistical bin limits on wafer level test bin data are used for minimizing value added to defective product as well as protecting end customers from potential quality and reliability excursion. Most wafer level test bin data show skewed distributions. By Monte Carlo simulation, this paper evaluates methods and sample size effect regarding determination of statistical bin limits. In the simulation, it is assumed that wafer level test bin data follow the Poisson distribution. Hence, typical shapes of the data distribution can be specified in terms of the distribution's parameter. This study examines three different methods; 1) percentile based methodology; 2) data transformation; and 3) Poisson model fitting. The mean square error is adopted as a performance measure for each simulation scenario. Then, a case study is presented. Results show that the percentile and transformation based methods give more stable statistical bin limits associated with the real dataset. However, with highly skewed distributions, the transformation based method should be used with caution in determining statistical bin limits. When the data are well fitted to a certain probability distribution, the model fitting approach can be used in the determination. As for the sample size effect, the mean square error seems to reduce exponentially according to the sample size.

Bayesian Analysis of a Zero-inflated Poisson Regression Model: An Application to Korean Oral Hygienic Data (영과잉 포아송 회귀모형에 대한 베이지안 추론: 구강위생 자료에의 적용)

  • Lim, Ah-Kyoung;Oh, Man-Suk
    • The Korean Journal of Applied Statistics
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    • v.19 no.3
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    • pp.505-519
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    • 2006
  • We consider zero-inflated count data, which is discrete count data but has too many zeroes compared to the Poisson distribution. Zero-inflated data can be found in various areas. Despite its increasing importance in practice, appropriate statistical inference on zero-inflated data is limited. Classical inference based on a large number theory does not fit unless the sample size is very large. And regular Poisson model shows lack of St due to many zeroes. To handle the difficulties, a mixture of distributions are considered for the zero-inflated data. Specifically, a mixture of a point mass at zero and a Poisson distribution is employed for the data. In addition, when there exist meaningful covariates selected to the response variable, loglinear link is used between the mean of the response and the covariates in the Poisson distribution part. We propose a Bayesian inference for the zero-inflated Poisson regression model by using a Markov Chain Monte Carlo method. We applied the proposed method to a Korean oral hygienic data and compared the inference results with other models. We found that the proposed method is superior in that it gives small parameter estimation error and more accurate predictions.

Grain distribution and electrical property according to grain size variation in polysilicon TFTs (다결정 실리콘 TFT소자의 채널길이 변화에 따른 grain의 분포와 전기적 특성)

  • Lee, Eun-Nyung;Song, Ho-Young;Park, Se-Geun;Lee, Taek-Joo;O, Beom-Hoan;Lee, Seung-Gol;Lee, El-Hang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2003.11a
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    • pp.128-131
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    • 2003
  • The number of grain is determined based on Poisson distribution in respectively different active channel and it is converted to grain size which affects to the mobility and threshold voltage. the acquired data is applied to the SPICE for observing the variation of I-V characteristic with several channel lengths. we can confirm the effect on device.

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Sample size calculations for clustered count data based on zero-inflated discrete Weibull regression models

  • Hanna Yoo
    • Communications for Statistical Applications and Methods
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    • v.31 no.1
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    • pp.55-64
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    • 2024
  • In this study, we consider the sample size determination problem for clustered count data with many zeros. In general, zero-inflated Poisson and binomial models are commonly used for zero-inflated data; however, in real data the assumptions that should be satisfied when using each model might be violated. We calculate the required sample size based on a discrete Weibull regression model that can handle both underdispersed and overdispersed data types. We use the Monte Carlo simulation to compute the required sample size. With our proposed method, a unified model with a low failure risk can be used to cope with the dispersed data type and handle data with many zeros, which appear in groups or clusters sharing a common variation source. A simulation study shows that our proposed method provides accurate results, revealing that the sample size is affected by the distribution skewness, covariance structure of covariates, and amount of zeros. We apply our method to the pancreas disorder length of the stay data collected from Western Australia.

Simulation Input Modeling : Sample Size Determination for Parameter Estimation of Probability Distributions (시뮬레이션 입력 모형화 : 확률분포 모수 추정을 위한 표본크기 결정)

  • Park Sung-Min
    • Journal of the Korean Operations Research and Management Science Society
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    • v.31 no.1
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    • pp.15-24
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    • 2006
  • In simulation input modeling, it is important to identify a probability distribution to represent the input process of interest. In this paper, an appropriate sample size is determined for parameter estimation associated with some typical probability distributions frequently encountered in simulation input modeling. For this purpose, a statistical measure is proposed to evaluate the effect of sample size on the precision as well as the accuracy related to the parameter estimation, square rooted mean square error to parameter ratio. Based on this evaluation measure, this sample size effect can be not only analyzed dimensionlessly against parameter's unit but also scaled regardless of parameter's magnitude. In the Monte Carlo simulation experiments, three continuous and one discrete probability distributions are investigated such as ; 1) exponential ; 2) gamma ; 3) normal ; and 4) poisson. The parameter's magnitudes tested are designed in order to represent distinct skewness respectively. Results show that ; 1) the evaluation measure drastically improves until the sample size approaches around 200 ; 2) up to the sample size about 400, the improvement continues but becomes ineffective ; and 3) plots of the evaluation measure have a similar plateau pattern beyond the sample size of 400. A case study with real datasets presents for verifying the experimental results.

Dimensioning leaky bucket parameters considering the cell delay variation (셀 지연 변이를 고려한 리키 버킷 계수 결정 방법)

  • 이준원;이병기
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.32A no.8
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    • pp.31-38
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    • 1995
  • In this paper, we consider the leaky bucket parameter dimensioning problem in the presence of the cell delay variation(CDV) which arises at the customer premises network dud to the multiplexing with other traffic streams. We consider an ATM multiplexer in which a single CBR stream and several heterogeneous VBR traffic streams are multiplexed. Choosing an MMPP model for the bursty traffic streams, we derive an (MMPP+DD)/D/1/K queueing model for the evaluation of the CDV experienced by the CBR stream. We first evaluate the equilibrium queue length distribution embedded at tagged-cell arrival-time instants, based on whcih we calcuate the inter-cell time distribution and the distribution kof the number of tagged-cell departures in an arbitrary interval. Then we apply the analysis to the dimensionging problem of the leaky bucket parameters, examining how the employed traffic model affects the determination of the bucket size. Through numerical examples, we confirm that the Poisson traffic model can underestimate the bucket size, thus causing a considerable blocking probability for compliant use cells while the MMPP model can optimally design the bucket size which keeps the blocking probability under the target value.

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High-accuracy quantitative principle of a new compact digital PCR equipment: Lab On An Array

  • Lee, Haeun;Lee, Cherl-Joon;Kim, Dong Hee;Cho, Chun-Sung;Shin, Wonseok;Han, Kyudong
    • Genomics & Informatics
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    • v.19 no.3
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    • pp.34.1-34.6
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    • 2021
  • Digital PCR (dPCR) is the third-generation PCR that enables real-time absolute quantification without reference materials. Recently, global diagnosis companies have developed new dPCR equipment. In line with the development, the Lab On An Array (LOAA) dPCR analyzer (Optolane) was launched last year. The LOAA dPCR is a semiconductor chip-based separation PCR type equipment. The LOAA dPCR includes Micro Electro Mechanical System that can be injected by partitioning the target gene into 56 to 20,000 wells. The amount of target gene per wells is digitized to 0 or 1 as the number of well gradually increases to 20,000 wells because its principle follows Poisson distribution, which allows the LOAA dPCR to perform precise absolute quantification. LOAA determined region of interest first prior to dPCR operation. To exclude invalid wells for the quantification, the LOAA dPCR has applied various filtering methods using brightness, slope, baseline, and noise filters. As the coronavirus disease 2019 has now spread around the world, needs for diagnostic equipment of point of care testing (POCT) are increasing. The LOAA dPCR is expected to be suitable for POCT diagnosis due to its compact size and high accuracy. Here, we describe the quantitative principle of the LOAA dPCR and suggest that it can be applied to various fields.

A Coordinator-based RFID Protocol to Avoid Reader Collision (코디네이터 기반 RFID 리더 충돌 회피 프로토콜)

  • Yang, Hoon-Gee
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.14 no.2
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    • pp.321-328
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    • 2010
  • This paper presents a coordinator-based TDMA reader protocol that can avoid the reader collision in a passive RFID system. In the proposed protocol, the coordinator can not only minimize the number of empty slots by efficiently allocating slots to readers incoming in Poisson distribution, but reduce latency time through the limited frame size. The proposed protocol can be implemented in either mobile or fixed mode through the slot structure to be described in the context. The simulation results show it works as suggested and the frame size limitation as well as the statistical distribution of incoming readers has a great impact on the overall slots and the average latency time.

Creep analysis of a rotating functionally graded simple blade: steady state analysis

  • Mirzaei, Manouchehr Mohammad Hosseini;Arefi, Mohammad;Loghman, Abbas
    • Steel and Composite Structures
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    • v.33 no.3
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    • pp.463-472
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    • 2019
  • Initial thermo-elastic and steady state creep deformation of a rotating functionally graded simple blade is studied using first-order shear deformation theory. A variable thickness model for cantilever beam has been considered. The blade geometry and loading are defined as functions of length so that one can define his own blade profile and loading using any arbitrary function. The blade is subjected to a transverse distributed load, an inertia body force due to rotation and a distributed temperature field due to a thermal gradient between the tip and the root. All mechanical and thermal properties except Poisson's ratio are assumed to be longitudinally variable based on the volume fraction of reinforcement. The creep behaviour is modelled by Norton's law. Considering creep strains in stress strain relation, Prandtl-Reuss relations, Norton' law and effective stress relation differential equation in term of effective creep strain is established. This differential equation is solved numerically. By effective creep strain, steady state stresses and deflections are obtained. It is concluded that reinforcement particle size and form of distribution of reinforcement has significant effect on the steady state creep behavior of the blade.