• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.349-355
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• 2007

In this paper we study some important properties of the bivariate generalized hypergeometric probability (BGHP) distribution by establishing the existence of all the moments of the distribution and by deriving recurrence relations for raw moments. It is shown that certain mixtures of BGHP distributions are again BGHP distributions and a limiting case of the distribution is considered.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.187-206
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• 2011

The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.495-505
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• 2018

The purpose of the present paper is to investigate Confluent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1109-1115
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• 2010

In this paper, exact confidence interval 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 performance of exact confidence interval estimates of hypergeometric parameter in terms of actual coverage probability by small sample Monte Carlo simulation.

• Journal of Korea Society of Industrial Information Systems
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• v.26 no.5
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• pp.37-54
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• 2021

In this study, a customized model (CM) for the efficient operation of cold chain logistics considering the hypergeometric distribution is proposed. The CM focuses on the segmentation market of ready-to-eat foods and juices made from fresh materials. Companies should determine the amount of production by predicting consumer preferences and quantity to ensure high-efficiency production. The CM is represented as a mathematical formulation and implemented using the genetic algorithm (GA). Addition, the relative weights of CM are calculated. Further, the calculated weights are applied to the GA. In the numerical experiment, hypergeometric distribution is used to calculate the relative weights between the range of production quantities and the customized amount. Experiment results are the values of relative weights and the comparison results by average values of handling cost, total cost and CPU time. Finally, the significance of this study is summarized and a future research direction is remarked in conclusion.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.2
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• pp.98-105
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• 2012

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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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.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.541-547
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• 2009

We consider distribution, reliability and moment of ratio in two independent beta random variables X and Y, and reliability and $K^{th}$ moment of ratio are represented by a mathematical generalized hypergeometric function. We introduce an approximate maximum likelihood estimate(AML) of reliability and right-tail probability in the beta distribution.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.671-684
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• 2021

The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions k - 𝓤𝓒𝓥^* (𝛽), k - 𝓢^*_p (𝛽), 𝓡 (𝛽), 𝓡^𝜏 (A, B), k - 𝓟𝓤𝓒𝓥^* (𝛽) and k - 𝓟𝓢^*_p (𝛽) in the open unit disc 𝕌.