Search Results (5)

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels, $\alpha =0.05$ and $\alpha =0.01$, we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Cramér–von Mises (CVM), Lilliefors (LF), and Shapiro–Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes $n=25,50,75,100,150,200,250,500,$ and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera. Full article

The performance of radio-frequency interference (RFI) detection and localization could be improved if they are applied on good quality inputs. RFI assessment is an important aspect of evaluating overall signal quality. The worthiness of a Global Navigation Satellite System (GNSS) receiver output can be generally quantified by a number of parameters readily available from a receiver. However, such discrete parameters do not give a detailed picture of the quality of the received GNSS signals. Statistical treatment of the received signals both in the absence and presence of interference gives some interesting insight about the data. In this paper, we study if the baseband data from the front-end Analog to Digital Converter (ADC) are normally distributed and if the presence of interference affects the statistical behavior of the distribution, often characterized by its probability density function (PDF) and other related parameters, such as skewness and kurtosis. In the second part of the paper, we study the feasibility of the Shapiro–Wilk (SW) test as a method to study the effect of interference on the GNSS signal while also serving as a potential approach to assess RFI. Skewness and kurtosis are statistical measures used to examine the shape of the distribution of a set of data. The implementation of the Shapiro–Wilk test is also studied, which is a normality test used to check whether a set of data follows a normal distribution. The above approaches have been evaluated using an experiment, where an RTLSDR is used as a reference GNSS receiver and simulated noise is added in the real signals. The data have been logged both in the presence and absence of wideband interference. The obtained results show the potential of the techniques presented for both the quantification of GNSS signal quality and the RFI assessment, alike. Full article

Testing the feasibility of soil phytoremediation requires the development of models applicable on a large scale. Phytoremediation mechanisms include advanced rhizosphere biodegradation, phytoaccumulation, phytodegradation, and phytostabilization. The aim of this study was to evaluate the phytoremediation potential of the Sinapis alba. Identification of the factors influencing the extraction process of metals from contaminated soils in a laboratory system suitable for evaluating the phytoavailability of these metals in three solutions (M1-CaCl₂, M2-DTPA, and M3-EDTA) included the following: distribution of metals in solution (Kd), soil properties and mobile fractions (SOC, CEC, pH), response surface methodology (RSM), and principal component analysis (PCA). The evaluation of the phytoremediation potential of the Sinapis alba plant was assessed using bioaccumulation coefficients (BACs). The accumulation of heavy metals in plants corresponds to the concentrations and soluble fractions of metals in the soil. Understanding the extractable metal fractions and the availability of metals in the soil is important for soil management. Extractable soluble fractions may be more advantageous in total metal content as a predictor of bioconcentrations of metals in plants. In this study, the amount of metal available in the most suitable extractors was used to predict the absorption of metals in the Sinapis alba plant. Multiple regression prediction models have been developed for estimating the amounts of As and Cd in plant organs. The performance of the predictive models generated based on the experimental data was evaluated by the adjusted coefficient of determination (aR2), model efficiency (RMSE), Durbin–Watson (DW) test, and Shapiro–Wilk (SW) test. The accumulation of the analyzed metals followed the pattern Root > Pods > Leaves > Seeds, stems > Flowers for As and Leaves > Root > Stem > Pods > Seeds > Flowers for Cd in soil contaminated with different metal concentrations. The obtained results showed a phytoremediation potential of the Sinapis alba plant. Full article

This study included the testing of normal (Gaussian) distribution of input data and, consequently, spatially interpolating maps of chemical components and cement modules in the flysch. This deposit contains the raw material for cement production. The researched area is located in southern Croatia, near Split, as part of the exploited field “St. Juraj–St. Kajo”. There are six lithological units: (1) alternation of marls and sandstones with inclusions of conglomerates, (2) marl, (3) calcsiltite, (4) calcarenite, (5) marl with nummulites, (6) debrites, and (7) clayey marl. All of them are deposited in the (a) northern and (b) southern beds. Only debrites are divided into the (a) western and (b) eastern layers. Those lithological units were divided technologically based on their cement modules (lime saturation factor (LSF), silicate module (SM), and aluminate module (AM)). The average thicknesses were analysed, followed by normality tests (Kolmogorov–Smirnov (K–S) and Shapiro–Wilk (S–W)) of the chemical analyses: CaO, SiO₂, Al₂O₃, Fe₂O₃, MgO, SO₃, Na₂O, K₂O, CaCO₃ (%) and three cement modules (LSF, SM, AM), available in the six lithological units. The normality tests were applied based on a number of input data. The further interpolation was performed using two methods, kriging and inverse distance weighting, mapping CaO (%), SiO₂ (%), and LSF (−) in three different lithological units. The interpolation methods were selected based on two criteria: (a) normality test pass or fail and (b) the amount of data. In total, 144 tests were calculated, including sets from 7 to 36 points. The results show the current situation in the quarry, after decades of production, making reliable the future predictions of cement raw material exploitation. Full article

The whole life cycle of an insulated gate bipolar transistor (IGBT) is a kind of asymmetry process, while the whole life cycles of a set of IGBTs can be regarded as a symmetry process. Modelling these symmetry characteristics of the IGBT life cycles enables the improvement of the remaining useful life (RUL) prediction performance. For this purpose, based on the key failure mechanism of IGBT in electric vehicles, a new method for estimating the RUL of an IGBT module is proposed based on the two-stress acceleration synthesis environment of junction temperature and vibration. The maximum likelihood estimation (MLE) was employed to estimate the logarithmic standard deviation and covariance matrix. The Shapiro–Wilk (S–W) test was performed to investigate the satisfaction degree of the RUL of the IGBT module to the lognormal distribution. The accelerated life test datasets of the IGBT module were analyzed using the Weibull++ software. The analysis results demonstrate that the IGBT lifetime is confirmed to lognormal distribution, and the accelerated model accords with the generalized Eyring acceleration model. The proposed method can estimate IGBT RUL in a short time, which provides a certain technical reference for the reliability analysis of the IGBT module. Full article