• Communications for Statistical Applications and Methods
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• v.31 no.6
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• pp.645-659
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• 2024

This study investigates the Charlier series approximation for modeling nonhomogeneous Poisson processes. It focuses on mixtures of Poisson distributions and Markov-Modulated Poisson processes to address complex temporal data patterns, such as hospital admission rates. The Charlier series approximation is constructed by expanding probability mass functions using Charlier orthogonal polynomials, which allow for adjustments to reflect higher-order moments like skewness and kurtosis. These polynomials are combined with a Poisson weight function to create flexible approximations tailored to the variability in event rates. Two artificial examples demonstrate the method's effectiveness in capturing dynamic event behaviors. A real-world application to hospital admission data further highlights its practical utility. Performance is assessed using Kullback-Leibler divergence, quantifying the improvement over simple Poisson models. The results show that the Charlier series provides enhanced data fitting and deeper insights into complex probabilistic structures.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.2
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• pp.91-106
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• 1992

It an inventory control system, the demand over time are often assumed to be independently identically distributed (i. i. d.). However, the demands may well be correlated over time in many situations. The estimation of reorder points is not simple for correlated demands with variable lead time. In this paper, a general class of autoregressive and moving average processes is considered for modeling the demands of an inventory item. The first four moments of the lead-time demand (L) are derived and used to approximate the distribution of L. The reorder points at given service level are then estimated by the three approximation methods : normal approximation, Charlier series and Pearson system. Numerical investigation shows that the Pearson system and the Charlier series performs extremely well for various situations whereas the normal approximation show consistent underestimation and sensitive to the distribution of lead time. The same conclusion can be reached when the parameters are estimated from the sample based on the simulation study.

• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.123-130
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• 1997

This paper presents a generalized expansion method for calculating reliability index in power generation systems. This generalized expansion with a gamma distribution is a very useful tool for the approximation of capacity outage probability distribution of generation system. The well-known Gram-Charlier expansion and Legendre series are also studied in this paper to be compared with this generalized expansion using a sample system IEEE-RTS(Reliability Test System). The results show that the generalized expansion with a composite of gamma distributions is more accurate and stable than Gram-Charlier expansion and Legendre series as addition of the terms to be expanded.