• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.505-513
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• 2011

In this paper, we obtain the derivations of moments of discrete probability distributions by using the backward difference operators. Also, we presents such derivations for several well-known distributions; they are the binomial, Poisson, geometric, hypergeometric and negative hypergeometric distributions.

• Journal of the Korea Society of Computer and Information
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• v.23 no.7
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• pp.99-104
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• 2018

In this paper, we compare Fisher's continuous method with an exact discrete analog of Fisher's continuous method from permutation tests for combining p values. The discrete analog of Fisher's continuous method is known to be adequate for combining independent p values from discrete probability distributions. Also permutation tests are widely used as alternatives to conventional parametric tests since these tests are distribution-free, and yield discrete probability distributions and exact p values. In this paper, we obtain permutation p values from discrete probability distributions using Mann-Whitney test data sets (real data and hypothetical data) and combine p values by the exact discrete analog of Fisher's continuous method.

• Journal of the Korea Society of Computer and Information
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• v.25 no.7
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• pp.175-182
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• 2020

Fisher's classical method for combining independent p-values from continuous distributions is widely used but it is known to be inadequate for combining p-values from discrete probability distributions. Instead, the discrete analog of Fisher's classical method is used as an alternative for combining p-values from discrete distributions. In this paper, firstly we obtain p-values from discrete probability distributions associated with multi-sample location test data (Fisher-Pitman test and Kruskall-Wallis test data) by permutation method, and secondly combine the permutaion p-values by the discrete analog of Fisher's classical method. And we finally compare the combined p-values from both the discrete analog of Fisher's classical method and Fisher's classical method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.51-64
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• 2012

This paper provides an efficient dimension reduction algorithm of the positive realization of discrete phase type(DPH) distributions. The relationship between the representation of DPH distributions and the positive realization of the positive system is explained. The dimension of the positive realization of a discrete phase-type realization may be larger than its McMillan degree of probability generating functions. The positive realization with sufficient large dimension bound can be obtained easily but generally, the minimal positive realization problem is not solved yet. We propose an efficient dimension reduction algorithm to make the positive realization with tighter upper bound from a given probability generating functions in terms of convex cone problem and linear programming.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.675-690
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• 1998

A role of singletons in quantum central limit theorems is studied. A common feature of quantum central limit distributions, the singleton condition which guarantees the symmetry of the limit distributions, is revisited in the category of discrete groups and monoids. Introducing a general notion of quantum independence, the singleton independence which include the singleton condition as an extremal case, we clarify the role of singletons and investigate the mechanism of arising non-symmetric limit distributions.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09b
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• pp.704-705
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• 2006

Discrete element analysis is used to map various log-normal particle size distributions into measures of the in-sphere pore size distribution. Combinations evaluated range from monosized spheres to include bimodal mixtures and various log-normal distributions. The latter proves most useful in providing a mapping of one distribution into the other (knowing the particle size distribution we want to predict the pore size distribution). Such metrics show predictions where the presence of large pores is anticipated that need to be avoided to ensure high sintered properties.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.10
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• pp.1144-1150
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• 2009

This paper investigates the feasibility of the Bayesian discrete time approximation method to estimate the parameters of Weibull distributions of failures for two non-identical components connected in series system. A Bayesian model based on the discrete time approximation method is formulated to infer the Weibull parameters of two non-identical components with the failure data of the virtual tests. The study of this paper comes to a conclusion that the method is feasible only for some special cases under the given constraints on the concerned parameters.

• Journal of the Korean Statistical Society
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• v.15 no.1
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• pp.71-78
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• 1986

In this paper, multivariate discrete distribution is dealt with, where a set of r distinct counts are misreported as another set of r counts. First, the variance for the one variable marginal case is expressed in the form of an inverted parabola. Next, for the multivariate negative binomial case, elements of the covariance matrix are evaluated with reference to asymptotic distributions. Finally, for the same case of multivariate negative binomial, Bayesian estimates of the parameters and of the modification rates are provided.