Probability Laws for Nearly Gaussian Random Variables and Application

• Type: Article in International Conference Proceedings Book
• Date: 2022-06-30

Authors

Rui Jorge Gonçalves (Author) FEUP

Conference proceedings International

Title: INNOVATIONS IN INDUSTRIAL ENGINEERING

Pages: 385-395

1st International Conference on Innovation in Engineering (ICIE)

Guimaraes, PORTUGAL, JUN 28-30, 2021

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ISI Web of Knowledge - 0 Citations

Other information

Authenticus ID: P-00W-DSZ

DOI: 10.1007/978-3-030-78170-5_33

Abstract (EN): In an earlier work we described and applied a methodology to find an adequate distribution for Nearly Gaussian (NG) random variables. In this work, we compare two different methods, m1 and m2 to estimate a power transform parameter for NG random variables. The m1 method is heuristic and based on sample kurtosis. Herein, we describe and apply it using a new reduced data set. The second method m2 is based on the maximization of a pseudo-log-likelihood function. As an application, we compare the performance of each method using high power statistical tests for the null hypothesis of normality. The data we use are the daily errors in the forecasts of maximum and minimum temperatures in the city of Porto. We show that the high kurtosis of the original data is due to high correlation among data. We also found that although consistent with normality the data is better fitted by distributions of the power normal (PN) family than by the normal distribution. Regarding the comparison of the two parameter estimation methods we found that the m1 provides higher p-values for the observed statistics tests except for the Shapiro-Wilk test.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 11