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Price-Based Scheduling for Gencos
Published in João P. S. Catalão, Electric Power Systems, 2017
Govinda B. Shrestha, Songbo Qiao
The three candidate distributions under consideration are normal, lognormal, and Weibull distributions. The tests are carried out for all three distributions at two different levels of significance (α = 0.05 and α = 0.01). The statistical tool box under MATLAB® is utilized for this purpose, which uses the Lilliefors test and the Kolmogorov–Smirnov test for hypothesis testing. The Lilliefors test is a two-sided goodness-of-fit test suitable when a fully specified null distribution is unknown and its parameters must be estimated. It is specific for the normal family distribution, in this case for the normal and lognormal distributions. Similarly, the Kolmogorov–Smirnov test is used for the Weibull distribution. Investigations are carried out to determine whether the price data can be characterized by any of the candidate distribution functions.
Developing pre-laboratory videos for enhancing student preparedness
Published in European Journal of Engineering Education, 2020
T. L. Rodgers, N. Cheema, S. Vasanth, A. Jamshed, A. Alfutimie, P. J. Scully
All the data collected in this paper is statistically tested, providing confidence in similarities and differences. For continuous data the normality of the distribution is checked using the Lilliefors test. The null hypothesis is that data come from a normally distributed population, where the null hypothesis does not specify which normal distribution; i.e. it does not specify the expected value and variance of the distribution; this means the critical values are lower than the one-sample Kolmogorov–Smirnov test, thus are more stringent. If the distributions are normal then the student t-test is used, if the distributions are not normal then a two-sample Kolmogorov–Smirnov test is also used with the t-test to provide added confidence. For data from Likert scales normality is not checked as the t-test provides good statistical representation regardless of distribution and number of samples (Norman 2010; Sullivan and Artino 2013). All t-test results are presented as a probability of likeliness of coming from the same distribution, p, for readability.
Enhancement signal detection in underwater acoustic noise using level dependent estimation time-frequency de-noising technique
Published in Journal of Marine Engineering & Technology, 2020
Yasin Yousif Al-Aboosi, Ahmad Zuri Sha’ameri, Adheed Hasan Sallomi
Two random variables, X and Y, are considered. X is a Gaussian random variable with mean , variance , and pdf ; is a t-distributed random variable with degrees of freedom, mean variance , and pdf (Nason 2006). The pdf for the sum of the random variables is (Ahsanullah et al. 2014) where ; Ψ(.) denotes Kummer’s hypergeometric function. By substituting and using the relationship between Kummer’s hypergeometric function and the complementary error function (Abramowitz and Stegun 1964), Subsequently, Eq. 19 is substituted into Eq. 18 to obtain Eq. 20 shows that the function approaches a Gaussian distribution as the variance or the degrees of freedom increases. A normality test, such as the Lilliefors test, is performed to determine if the pdf of the sum of the random variables is approximately Gaussian (Lilliefors 1969; Conover and Conover 1980). If the degree of freedom is greater than 1, the pdf in Eq. 22 is approximately Gaussian. The threshold derived from the can be calculated by Eq. 11. The can be calculated by the threshold defined in Eq. 13.