• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.463-484
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• 2023

An examination is conducted on the multinomial coefficients derived from generalized quantum deformed algebras, and on their recurrence relations. The 𝓡(p, q)-deformed multinomial probability distribution and the negative 𝓡(p, q)-deformed multinomial probability distribution are constructed, and the recurrence relations are determined. From our general result, we deduce particular cases that correspond to quantum algebras considered in the literature.

• Journal of the Korean Data and Information Science Society
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• 제23권2호
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• pp.411-417
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• 2012

In this paper, we consider the estimation of multinomial proportions. Multinomial distribution is the most important multivaritate distribution. Estimation of multinomial parameters for multinomial distribution is widely applicable to many practical research areas including genetics. We investigated the properties of several frequency substitution estimates and derived the maximum likelihood estimate of multinomial proportions of Hardy Weinberg proportions. Phenotype and genotype frequencies of allele are used to the estimation of multinomial proportions. These estimates are then analyzed via numerical data. Small sample Monte Carlo simulation is conducted to compare considered estimates of multinomial proportions.

• Journal of the Korean Data and Information Science Society
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• 제7권1호
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• pp.105-112
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• 1996

Softwares including random number generation are abundant in modern informative society. But it's hard to get directly multivariate multinomial random numbers from existing softwares. Multivariate multinomial random numbers are greatly used in social and medical sciences. In this paper, we show that desired multivariate multinomial random numbers can be easily generated by the aids of existing random number generating software. Some characteristics of multivariate multinomial distribution are surveyd. Measures of association for the generated random numbers were computed and compared with population ones via simulation study.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.121-131
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• 2007

In this paper, we examine the problem of estimating the sensitive characteristics and behaviors in a multinomial randomized response model using Bayesian approach. We derived a posterior distribution for parameter of interest for multinomial randomized response model. Based on the posterior distribution, we also calculated a credible intervals and mean squared error (MSE). We finally compare the maximum likelihood estimator and the Bayes estimator in terms of MSE.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.239-244
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• 2005

In this paper, we examine the problem of estimating the sensitive characteristics and behaviors in a multinomial randomized response (RR) model. We analyze this problem through a Bayesian perspective and develop a Bayesian multinomial RR model in survey study. The Bayesian inference of multinomial RR model is a new approach to RR models.

• Journal of the Korean Statistical Society
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• 제13권1호
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• pp.1-19
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• 1984

A random effects model of a one-way layout contingency table is developed using a Dirichlet-multinomial distribution. A test statistic, say $T_k$, is suggested for detecting Dirichlet-multinomial departure from a multinomial distribution. It is shown that the $T_k$ test is asymptotically superior to the classical chi-square test based on the asymptotic relative efficiency. This superiority is further evidenced by a Monte Carlo simulation.

• 유통과학연구
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• 제14권11호
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• pp.61-73
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• 2016

Purpose - Marketing scholars have developed various types of mathematical models for describing marketing phenomenon, because there is no single model comprehensive enough to incorporate all the relevant marketing phenomena. This study tries to summarize the behavioral foundations and the mathematical derivations of the most widely used marketing models and discusses their strategic implications. This study selected four representative marketing models: multinomial logit(MNL) model, elimination-by-aspects(EBA) model, Hauser and Shugan model and Bass diffusion model. Especially, this study focuses on Hauser and Shugan(1983)'s Defender model and discusses the model's behavioral foundation and its implications. Research design, data, and methodology - Of the four selected model, the multinomial logit model is selected as the basic normative model and the other three models are described as descriptive models in contrast. Starting the discussion from the multinomial logit model, this study explains what important strategic variables are incorporated in each of the four models. The IIA(independence of irrelevant alternatives) axiom and Luce choice model is also discussed in relation to the multinomial logit model. The concept of 'efficient frontier' is discussed in relation to Hauser and Shugan's model. Graphs and tables are used to represent the key implications. No empirical study is included. Results - The analyses of the mathematical marketing models are shown to be very useful in understanding the essence of positioning strategy. The multinomial logit model implies the importance of increasing utility or consumer preference level. The EBA model implies the importance of lowering the inter-brand similarity and dominating the competitors. Hauser and Shugan model implies the importance of considering customer heterogeneity distribution in selecting the target market. Conclusions - It is shown that the concepts of 'efficient frontier' is useful in understanding the effectiveness of positioning strategy. Market positioning can be understood as occupying some place on the efficient frontier. The important strategic implications can be summarized as follows: Always try to increase customer preference by providing what they value, and differentiate from competing alternatives as much as possible. The best positioning strategy is to dominate all the competitors and the worst is to be dominated by the competitors.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.125-137
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• 2005

Many discriminant analysis models for binary data have been used in real applications, but none of the classification models dominates in all varying circumstances(Asparoukhov & Krzanowski(2001)). Lee and Hwang (2003) proposed a new classification model by using multinomial distribution with the maximum entropy estimation method. The model showed some promising results in case of small number of variables, but its performance was not satisfactory for large number of variables. This paper explores to use the iterative cross entropy minimization estimation method in replace of the maximum entropy estimation. Simulation experiments show that this method can compete with other well known existing classification models.

• Communications for Statistical Applications and Methods
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• 제10권2호
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• pp.525-534
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Journal of the Korean Statistical Society
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• 제27권2호
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• pp.197-203
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• 1998

To test the hypothesis of complete or total independence for a multi-way contingency table, the Pearson chi-squared test statistic is usually employed under Poisson or multinomial models. It is well known that, under the hypothesis, this statistic follows an asymptotic chi-squared distribution. We consider the case where all marginal sums of the contingency table are fixed. Using conditional limit theorems, we show that the chi-squared test statistic has the same limiting distribution for this case.