• Title/Summary/Keyword: Binomial

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Comparison of Three Binomial-related Models in the Estimation of Correlations

  • Moon, Myung-Sang
    • Communications for Statistical Applications and Methods
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    • v.10 no.2
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    • pp.585-594
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    • 2003
  • It has been generally recognized that conventional binomial or Poisson model provides poor fits to the actual correlated binary data due to the extra-binomial variation. A number of generalized statistical models have been proposed to account for this additional variation. Among them, beta-binomial, correlated-binomial, and modified-binomial models are binomial-related models which are frequently used in modeling the sum of n correlated binary data. In many situations, it is reasonable to assume that n correlated binary data are exchangeable, which is a special case of correlated binary data. The sum of n exchangeable correlated binary data is modeled relatively well when the above three binomial-related models are applied. But the estimation results of correlation coefficient turn to be quite different. Hence, it is important to identify which model provides better estimates of model parameters(success probability, correlation coefficient). For this purpose, a small-scale simulation study is performed to compare the behavior of above three models.

Tilted beta regression and beta-binomial regression models: Mean and variance modeling

  • Edilberto Cepeda-Cuervo
    • Communications for Statistical Applications and Methods
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    • v.31 no.3
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    • pp.263-277
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    • 2024
  • This paper proposes new parameterizations of the tilted beta binomial distribution, obtained from the combination of the binomial distribution and the tilted beta distribution, where the beta component of the mixture is parameterized as a function of their mean and variance. These new parameterized distributions include as particular cases the beta rectangular binomial and the beta binomial distributions. After that, we propose new linear regression models to deal with overdispersed binomial datasets. These new models are defined from the proposed new parameterization of the tilted beta binomial distribution, and assume regression structures for the mean and variance parameters. These new linear regression models are fitted by applying Bayesian methods and using the OpenBUGS software. The proposed regression models are fitted to a school absenteeism dataset and to the seeds germination rate according to the type seed and root.

Markov Chain Approach to Forecast in the Binomial Autoregressive Models

  • Kim, Hee-Young;Park, You-Sung
    • Communications for Statistical Applications and Methods
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    • v.17 no.3
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    • pp.441-450
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    • 2010
  • In this paper we consider the problem of forecasting binomial time series, modelled by the binomial autoregressive model. This paper considers proposed by McKenzie (1985) and is extended to a higher order by $Wei{\ss}$(2009). Since the binomial autoregressive model is a Markov chain, we can apply the earlier work of Bu and McCabe (2008) for integer valued autoregressive(INAR) model to the binomial autoregressive model. We will discuss how to compute the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$ when T periods are used in fitting. Then we obtain the maximum likelihood estimator of binomial autoregressive model and use it to derive the maximum likelihood estimator of the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$. The methodology is illustrated by applying it to a data set previously analyzed by $Wei{\ss}$(2009).

The Origin of Newton's Generalized Binomial Theorem (뉴턴의 일반화된 이항정리의 기원)

  • Koh, Youngmee;Ree, Sangwook
    • Journal for History of Mathematics
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    • v.27 no.2
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    • pp.127-138
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    • 2014
  • In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.

THE LIMITING LOG GAUSSIANITY FOR AN EVOLVING BINOMIAL RANDOM FIELD

  • Kim, Sung-Yeun;Kim, Won-Bae;Bae, Jong-Sig
    • Communications of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.291-301
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    • 2010
  • This paper consists of two main parts. Firstly, we introduce an evolving binomial process from a binomial stock model and consider various types of limiting behavior of the logarithm of the evolving binomial process. Among others we find that the logarithm of the binomial process converges weakly to a Gaussian process. Secondly, we provide new approaches for proving the limit theorems for an integral process motivated by the evolving binomial process. We provide a new proof for the uniform strong LLN for the integral process. We also provide a simple proof of the functional CLT by using a restriction of Bernstein inequality and a restricted chaining argument. We apply the functional CLT to derive the LIL for the IID random variables from that for Gaussian.

Coherent Forecasting in Binomial AR(p) Model

  • Kim, Hee-Young;Park, You-Sung
    • Communications for Statistical Applications and Methods
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    • v.17 no.1
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    • pp.27-37
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    • 2010
  • This article concerns the forecasting in binomial AR(p) models which is proposed by Wei$\ss$ (2009b) for time series of binomial counts. Our method extends to binomial AR(p) models a recent result by Jung and Tremayne (2006) for integer-valued autoregressive model of second order, INAR(2), with simple Poisson innovations. Forecasts are produced by conditional median which gives 'coherent' forecasts, and we estimate the forecast distributions of future values of binomial AR(p) models by means of a Monte Carlo method allowing for parameter uncertainty. Model parameters are estimated by the method of moments and estimated standard errors are calculated by means of block of block bootstrap. The method is fitted to log data set used in Wei$\ss$ (2009b).

Sensory Difference Testing: The Problem of Overdispersion and the Use of Beta Binomial Statistical Analysis

  • Lee, Hye-Seong;O'Mahony, Michael
    • Food Science and Biotechnology
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    • v.15 no.4
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    • pp.494-498
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    • 2006
  • An increase in variance (overdispersion) can occur when a binomial statistical analysis is applied to sensory difference test data in which replicate sensory evaluations (tastings) and multiple evaluators (judges) are combined to increase the sample size. Such a practice can cause extensive Type I errors, leading to serious misinterpretations of the data, especially when traditional simple binomial analysis is applied. Alternatively, the use of beta binomial analysis will circumvent the problem of overdispersion. This brief review discusses the uses and computation methodology of beta binomial analysis and in practice evidence for the occurrence of overdispersion.

A maximum likelihood estimation method for a mixture of shifted binomial distributions

  • Oh, Changhyuck
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.1
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    • pp.255-261
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    • 2014
  • Many studies have estimated a mixture of binomial distributions. This paper considers an extension, a mixture of shifted binomial distributions, and the estimation of the distribution. The range of each component binomial distribution is rst evaluated and then for each possible value of shifted parameters, the EM algorithm is employed to estimate those parameters. From a set of possible value of shifted parameters and corresponding estimated parameters of the distribution, the likelihood of given data is determined. The simulation results verify the performance of the proposed method.

RECURRENCE RELATIONS FOR HIGHER ORDER MOMENTS OF A COMPOUND BINOMIAL RANDOM VARIABLE

  • Kim, Donghyun;Kim, Yoora
    • East Asian mathematical journal
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    • v.34 no.1
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    • pp.59-67
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    • 2018
  • We present new recurrence formulas for the raw and central moments of a compound binomial random variable. Our approach involves relating two compound binomial random variables that have parameters with a difference of 1 for the number of trials, but which have the same parameters for the success probability for each trial. As a consequence of our recursions, the raw and central moments of a binomial random variable are obtained in a recursive manner without the use of Stirling numbers.

Embedding Complete binary trees in Binomial trees (완전이진트리의 이항트리에 대한 임베딩)

  • 윤수민;최정임형석
    • Proceedings of the IEEK Conference
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    • 1998.06a
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    • pp.289-292
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    • 1998
  • Trees are the underlying structure for divide-and-conquer algorithms and the graphs that provide the solution spaces for NP-complete problems. Complete binary trees are the basic structure among trees. Therefore, if complete binary trees can be embedded in binomial trees, the algorithms which are provided by complete binary trees can be performed efficiently on the interconnection networks which have binomial trees as their subgraphs or in which binomial trees can be embedded easily. In this paper, we present dilation 2 embedding of complete binary trees in binomial trees.

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