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Power Exponential Distributions
Zheng, Shimin,Bae, Sejong,Bartolucci, Alfred A.,Singh, Karan P. The Korean Reliability Society 2003 International Journal of Reliability and Applicati Vol.4 No.3
By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.
효율적인 오수처리시설 제어를 위한 퍼지 전문가 시스템 연구
임총규,박주식,Singh, Karan P.,Bae, SeJong 대한설비관리학회 2004 대한설비관리학회지 Vol.9 No.3
Dissolved oxygen (DO) and pH sensors were added to sequence batch reactor (SBR) to achieve highly efficient and reliable discharge water quality and treatment time. In this study, the fuzzy expert system was used to improve existing DO and pH control unit for effective sewage disposal control. The system utilized settled sludge layer in influent wastewater to maximize denitrificaton rate by controlling DO and pH levels in a tank. By providing adequate solids retention time, elimination of floating materials as well as denitrification and phosphorus removal were achieved in small wastewater treatment system. The system also reduced odor by controlling the production of ammonia in a sewage disposal equipment.