• Journal of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.101-123
• /
• 2001

For a linear operator Q from R(sup)d into R(sup)d and 0$\alpha$ and parameter b on the other. characterization of strictly (Q,b)-semi-stable distributions among (Q,b)-semi-stable distributions is made. Existence of (Q,b)-semi-stable distributions which are not translation of strictly (Q,b)-semi-stable distribution is discussed.

• Proceedings of the Korea Society for Simulation Conference
• /
• 2001.10a
• /
• pp.359-364
• /
• 2001

In this study, we try to improve the accuracy of QN-GPH by the help of simulation approach. We first establish an estimation method for GPH distributions with sufficient accuracy based on empirical distribution, and then perform a brief trial run to find appropriate empirical distributions. After getting GPH form of distributions, we continue the QN-GPH analytic steps and compute necessary performance measures. We apply the method to find sojourn time distributions in a 8-node queueing system and compare the results with the whole simulation and the original two-parametric approximation.

• Proceedings of the Polymer Society of Korea Conference
• /
• 2006.10a
• /
• pp.113-113
• /
• 2006

Polymer separations are used to obtain information on molecular distributions (molecular-weight distribution, chemical-composition distribution, functionality-type distribution, etc.). The existing methods, such as size-exclusion chromatography are reliable, but imperfect. New methods and improvements to existing methods are being studied and some of the results will be discussed. In addition, comprehensive two-dimensional liquid chromatography allows the complete characterization of two mutually dependent distributions. LCxSEC chromatograms provide a very good qualitative impression of the distributions, but calibration is not straightforward. Finally, progress in mass spectrometry allows much better information to be obtained.

• Honam Mathematical Journal
• /
• v.30 no.1
• /
• pp.185-195
• /
• 2008

We consider a system of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions and Gelfand generalized functions. As a consequence we find locally integrable solutions of the n-dimensional trigonometric functional equation.

• International Journal of Reliability and Applications
• /
• v.7 no.1
• /
• pp.55-69
• /
• 2006

This paper presents a new class of multivariate distributions with Pareto where dependence among the components is characterized by a latent random variable. The new class includes several multivariate and bivariate models of Marshall and Olkin type. It is found the bivariate distribution with Pareto is positively quadrant dependent and its mixture. Some important structural properties of the bivariate distributions with Pareto are discussed. The distribution of minimum in a competing risk Pareto model is derived.

• International Journal of Reliability and Applications
• /
• v.7 no.1
• /
• pp.13-25
• /
• 2006

A new class of life distributions is studied. This class is defined based on comparing the residual life time to the whole life in the moment generating function order giving 'the new better than used in the moment generating function order ageing class $(NBU_{mgf})$'. Fundamental properties of this class are given including some closure properties and characterizations. Finally, we consider new results about comparisons of age and block replacement policies when the underlying distribution belongs to $NBU_{mgf}$ aging classes.

• Journal of the Korean Statistical Society
• /
• v.33 no.1
• /
• pp.35-58
• /
• 2004

For fixed positive integers and $\textit{k}\;(n\;{\geq}\;{\textit{k}}\;+\;2)$, the exact probability distributions of non-overlapping and overlapping patterns of two failures separated by (i) exactly $textsc{k}$ successes, (ii) at least $\textit{k}$ successes and (iii) at most $\textit{k}$ successes have been obtained for Bernoulli independent and Markov dependent trials by using combinatorial technique. The waiting time distributions for the first occurrence and the $r^{th}$ (r > 1) occurrence of the patterns have also been obtained.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.22 no.1
• /
• pp.87-99
• /
• 1997

This paper considers warranty servicing for repairable products when product lifetimes are phase-type(PH) distributions. Two replace-repair strategies are analyzed based on renwal processes. The quantities of interest can be expressed in terms of the renewal function which, in general, is very difficult to evaluate. By exploiting properties of PH distributions we obtain simplification to evaluate these performance measures. Numerical examples for four different PH distributions with typical functions are presented and the results are discussed.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.325-335
• /
• 2002

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the center of symmetric and continuous underlying distributions. This selector statistics is based on the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying distributions. In this paper, we use the functions of sample quantiles as selector statistics and determine the suitable quantile points based on maximizing the distance index to discriminate distributions under consideration. In Monte Carlo study, this robust estimation method works pretty good in wide range of underlying distributions.

• Proceedings of the Korean Society for Agricultural Machinery Conference
• /
• 1996.06c
• /
• pp.1073-1080
• /
• 1996

The impact of the input and output probability distributions on the performance of neural networks to forecast two year peak stream flow (cubic meters per second) is examined for two major river basins of the US. The neural network input consisted of drainage area(square kilometers ) and elevation (meters). When data are normally distributed , the neural networks predict much better than when the data are non-normal and have larger tails in their distributions.