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This paper proposes a bias-corrected expression for maximum likelihood estimators using the sequential number-theoretic method for optimization (SNTO) to improve the efficiency and accuracy of the estimators in three extreme value distributions (EVDs). It is well known that the widely used maximum likelihood estimation (MLE) could be often biased for small-size samples in EVDs. Meanwhile, numerical simulation results reveal that maximum likelihood estimators are suffered from high variance when the sample size is small and the impact is non-negligible. A comprehensive comparison study which includes classical bias-corrected methods and more recent ones is presented. Based on the simulation studies, the bias-correction estimator via SNTO is highly recommended to reduce the bias and variance of estimators. In addition, a real data set is illustrated to employ different techniques. [ABSTRACT FROM AUTHOR]

The NCTU micro-orifice cascade impactor (NMCI) was redesigned and tested to enable the measurement and adjustment of the jet-to-plate distance (S) of the impactors by using a micrometer. Each stage of the NMCI contains an impaction plate and a nozzle plate which are separated. The bottom casing for impaction plate assembly and the nozzle plate holder of each stage are separated. Calibration results show that the cutoff aerodynamic diameter (dpa50) of the three lower stages (dpa50= 180, 100, and 56 nm) are close to the nominal values given in Marple et al. (1991). In addition, theS/W(W: nozzle diameter) effects on thedpa50for the three lower stages were investigated and an empirical equation was developed to facilitate the prediction ofdpa50when the nozzle diameters may change slightly from one batch to another. The relationship between the nozzle diameter and pressure drop of the micro-orifice impactors at the fixed operational flow rate of 30 L/min was also established so that the nozzle diameters can be predicted from the pressure drop measurement. An empirical equation was proposed to express the correlation between the dimensionless cutoff size and theS/Wratio when considering isentropic flow to facilitate the design of micro-orifice impactors forS/W> 4. It is expected that the present NMCI could improve the accuracy of size classification of submicron particles below 180 nm, especially for nanoparticles. Copyright 2015 American Association for Aerosol Research [ABSTRACT FROM PUBLISHER]

AbstractHypothesis testing for the Weibull distribution always raises attention in the literature. It is challenging especially in small-sample scenarios. In this paper, we propose a new Kolmogorov-Smirnov type test based on the distance between two empirical functions, one from the data and another from the representative points of the underlying distribution. A bias correction technique is used to estimate unknown parameters in the Weibull distribution. We also discuss how to choose a suitable number of representative points based on the proposed loss function, which is recommended for constructing the empirical function from the Weibull distribution. To compare with tailor-made tests in the literature, a simulation study of the empirical type I error and testing power is conducted. It shows that our proposed test statistic is more powerful in most alternative scenarios, and it significantly improves the power of testing in small-sample scenarios. Finally, two real-world datasets are conducted to further demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]