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Basic Notions of Statistics
Published in Piotr Konieczka, Jacek Namieśnik, Quality Assurance and Quality Control in the Analytical Chemical Laboratory, 2018
Piotr Konieczka, Jacek Namieśnik
Mathematical statistics is a branch of mathematics that applies the theory of probability to examining regularities in the occurrence of certain properties of material objects or phenomena which occur in unlimited quantities. Statistics presents these regularities by means of numbers.
Quantitative analysis and co-optimization of cathode catalyst layer compositions and operating conditions on cost and performance of PEM fuel cell
Published in International Journal of Green Energy, 2023
Xiongping Lin, Ruoyu Dai, Yiming Xu, Jieqing Zheng
The orthogonal numerical test is an effective analysis method for the multiple influential factors based on probability theory and mathematical statistics. As mentioned before, both range analysis and variance analysis should be conducted based on the results of orthogonal tests. In this paper, the operating conditions including temperature (T), anode humidity (RHa), cathode humidity (RHc), voltage (V), and CCL composition parameters including platinum loading (Mpt) and mass ratio of ionomer to carbon (Ric) are selected as the influential factors. The values of factors and levels are listed in Table 6. According to the factors and corresponding levels, the orthogonal numerical test table L28 (36) in Table 2 is designed. To evaluate each group of combinations, the unit power price (UPP, $/kW) and net power (NP, kW) are obtained using the finite difference model (Table 7).
Low-speed sensorless control of permanent magnet synchronous motors via the Cauchy–Gauss hybrid mutation particle swarm optimization algorithm
Published in Engineering Optimization, 2022
Changfu Gong, Rongyun Zhang, Peicheng Shi, Linfeng Zhao, Xinghui Fang, Chenglong Zhou
In probability theory and mathematical statistics, the Cauchy distribution is a continuous probability distribution with no expectation value. The probability density function of the one-dimensional Cauchy distribution can be expressed as where is a coefficient greater than zero. (When , Equation 28 is the standard Cauchy distribution.) The distribution function of the one-dimensional Cauchy distribution is The Gaussian distribution, by contrast, is ‘bell shaped’: low at both ends, high in the middle, and symmetrical to the left and right. The probability density function of the Gaussian distribution with expectation value μ and standard deviation σ is Its distribution function is (In the case μ = 0, σ = 1, Equation 31 is the standard Gaussian distribution.)
Optimal Batch Size Growth for Wielandt Method and Superhistory Method
Published in Nuclear Science and Engineering, 2022
Qingquan Pan, Tengfei Zhang, Xiaojing Liu, Yun Cai, Lianjie Wang, Kan Wang
Therefore, the error in the fission source first comes from the error in the guessed initial fission source. At the same time, the MC method is based on probability theory and mathematical statistics, so there is also a statistical error in the fission source. If the total number of simulated neutrons is h, then the statistical error is of the order . We have to say that there is a covariance between the adjacent cycles of the MC criticality calculation. The covariance will lead to the underestimation of variance, and the relation cannot be strictly satisfied. However, the covariance between the adjacent cycles of the MC criticality calculation is unavoidable. The source convergence acceleration methods are usually studied without considering the covariance. Therefore, in this paper the influence of the covariance on the improved Wielandt/Superhistory methods is not considered.