• 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 Chungcheong Mathematical Society
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• v.13 no.2
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• pp.19-27
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• 2001

In this paper we study another kind of the large deviation property, i.e. moderate deviation type for random amount of random measures on $R^d$ about a Poisson point process and a Poisson center cluster random measure.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.387-394
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• 2004

Zero-Inflated Poisson distribution is Poisson distribution with excess zeros. Recently defects of product hardley happen in the manufacturing process. In this case it is desirable to apply to the Zero-Inflated Poisson distribution rather than Poisson. Our target of this paper is to study the tests for changes of rate of defects after the unknown change-point. We are going to compare the powers of the two proposed tests with likelihood tests by the simulations.

• Journal of Korea Water Resources Association
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• v.41 no.7
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• pp.747-759
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• 2008

This study, a point rainfall process model, which could represent appropriately observed rainfall data, was to select. The point process models-rectangular pulses Poisson process model(RPPM), Neyman-Scott rectangular pulses Poisson process model(NS-RPPM), and modified Neyman-Scott rectangular pulses Poisson process model(modified NS-RPPM)-all based on Poisson process were considered as possible rainfall models, whose statistical analyses were performed with their simulation rainfall data. As results, simulated rainfall data using the NS-RPPM and the modified NS-RPPM represent appropriately statistics of observed data for several aggregation levels. Also, simulated rainfall data using the modified NS-RPPM shows similar characteristics of rainfall occurrence to the observed rainfall data. Especially, the modified NS-RPPM reproduces high-intensity rainfall events that contribute largely to occurrence of natural harzard such as flood and landslides most similarly. Also, the modified NS-RPPM shows the best results with respect to the total rainfall amount, duration, and inter-event time. In conclusions, the modified NS-RPPM was found to be the most appropriate model for the long-term simulation of rainfall.

• International Journal of Quality Innovation
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• v.5 no.1
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• pp.1-9
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• 2004

The nonhomogeneous poisson process (NHPP) is often used to model repairable systems that are subject to a minimal repair strategy, with negligible repair times. In this situation, the system can be characterized by its intensity function. There have been many NHPP models according to intensity functions. However, the intensity function of system in use can be changed because of repair or its aging. We consider the single change point model as the modification of the power law process. The shape parameter of its intensity function is changed before and after the change point. We detect the presence of the change point using Bayesian methodology. Some numerical results are also presented.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1083-1101
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• 2022

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admit a unique solution which belongs to class 𝔻.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.511-518
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• 2009

We consider the problem of testing for change and estimating the unknown change-point in a sequence of time-ordered observations from the binomial and Poisson distributions. Including the likelihood ratio test, Gombay and Horvath (1990) tests are studied and the proposed change-point estimator is derived from their test statistic. A power study of tests and a comparison study of change-point estimators are done via simulation.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
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• v.10 no.1
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• pp.33-39
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• 2011

This paper considers a performance analysis of set-top box (STB) power saving schemes. STB converts the signal into content which is then displayed on the television (TV) screen, and there are typically two operation modes: on mode and stand-by mode. The total energy consumption (TEC), a typical measure of power consumption of STB, is defined by the sum of power consumption in each mode. Recently there are some works of STB power saving schemes that transit STB operation modes efficiently, and the mode transition time point of those schemes can be different. Thus it is required to develop a performance evaluation method that reflects mode transition time points of each scheme to get TEC correctly. This paper proposes a performance evaluation method for STB power consumption using Poisson process to consider the mode transition time point. By modeling STB mode transitions as events of Poisson process, the average time duration of STB mode is computed and accordingly the effect of power saving is evaluated. The performance evaluation result shows that the proposed method achieves 1 to 19% improvement in power consumption compared with a conventional performance evaluation method.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.261-269
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• 2015

Nowadays the application of change point analysis has been indispensable in a wide range of areas such as quality control, finance, environmetrics, medicine, geographics, and engineering. Identification of times where process changes would help minimize the consequences that might happen afterwards. The main objective of this paper is to compare the change-point detection capabilities of Bayesian estimate and maximum likelihood estimate. We applied Bayesian and maximum likelihood techniques to formulate change points having a step change and multiple number of change points in a Poisson rate. After a signal from c-chart and Poisson cumulative sum control charts have been detected, Monte Carlo simulation has been applied to investigate the performance of Bayesian and maximum likelihood estimation. Change point detection capacities of Bayesian and maximum likelihood estimation techniques have been investigated through simulation. It has been found that the Bayesian estimates outperforms standard control charts well specially when there exists a small to medium size of step change. Moreover, it performs convincingly well in comparison with the maximum like-lihood estimator and remains good choice specially in confidence interval statistical inference.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.71-80
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• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.