Abstract
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.

Abstract
The Power Normal (PN) family of distributions is obtained by inverting the Box-Cox (BC) transformation over a truncated normal (TN) (or for some cases normal) random variable. In this paper we explore the PN distribution. We give a formula for the ordinary moments and considering the bivariate PN (BPN) distribution we calculate the marginal and conditional probability density functions (pdf). We prove that they are not univariate PN distributed. We also calculate the correlation curve and we fit a power law model.

Abstract

Abstract

Abstract
A probabilistic framework is defined to evaluate the values of the Confidence Factors (CFs) proposed in Eurocode 8 Part 3 (EC8-3) for the characterization of material properties. This evaluation is presented for the concrete compressive strength but its validity for other material properties can also be inferred from the results obtained. The number of material tests and the existence of prior knowledge are the essential aspects for the CF quantification. The probabilistic framework proposed in the first part of the study does not consider the existence of prior knowledge and is based on the concept of confidence intervals. In the second part of the study, the effects of prior knowledge are considered using a Bayesian framework. The combination of testing data obtained from different types of tests is also addressed as an extension of the referred Bayesian approach. Results indicate that the EC8-3 proposed CFs for KL1 and KL2 are adequate, but for KL3 it is suggested that a larger value should be used.