• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1549-1566
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• 2016

Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.273-281
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• 1996

It is derived that conditions of counting process ($\{N(t){\mid}t\;{\geq}\;0\}$) in which the number of events in time interval [0, t] has a (n, n+1)-generalized Poisson distribution with parameters (${\theta}t,\;{\lambda}$) and a generalized inflated Poisson distribution with parameters (${\{\lambda}t,\;{\omega}\}$.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.793-798
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• 2008

Extreme value inference deals with fitting the generalized extreme value distribution model and the generalized Pareto distribution model, which are recently combined to give a single model, namely a two-dimensional non-homogeneous Poisson exceedance point process model. In this paper, we extend the two-dimensional non-homogeneous Poisson process model to include non-stationary effect or dependence on covariates and then derive the likelihood for the extended model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.55-72
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• 2009

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability $\alpha$, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.353-364
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• 1999

We found the characterizations for convolution operators in the Beurling`s generalized distribution space to be hyperbolic.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.269-286
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• 2015

In this paper, we extend the concept of the pseudo differential operators in the usual Schwartz's distribution spaces to the one of the generalized pseudo differential operators in the Beurling's generalized distribution spaces. And we shall investigate some properties of the generalized pseudo differential operators including the generalized pseudo local property. Finally, we will study the smoothness and properly supported property of these operators.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.99-106
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• 2008

In this paper, we establish some recurrence relations which is satisfied by the quotient moments of the lower record values from the standard generalized extreme value (GEV) distribution.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.159-173
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• 2020

In this paper we define a new generalized polynomials of derangements. It also derives the differential equations that occur in the generating function of the generalized polynomials of derangements. We establish some new identities for the generalized polynomials of derangements. Finally, we perform a survey of the distribution of zeros of the generalized polynomials of derangements.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.75-93
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• 2008

The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.477-493
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• 2017

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and lower records are deduced from the relations derived and some computational works are also carried out. Further, a characterizing result of this distribution on using the conditional moment of the dual generalized order statistics is discussed. These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, skewness and kurtosis of order statistics and record values of the Dagum distribution.