Skewness and kurtosis comparisons of continuous distributions

Author(s):  
Robert A. Rigby ◽  
Mikis D. Stasinopoulos ◽  
Gillian Z. Heller ◽  
Fernanda De Bastiani
Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 19 ◽  
Author(s):  
Roser Bono ◽  
Jaume Arnau ◽  
Rafael Alarcón ◽  
Maria J. Blanca

Several measures of skewness and kurtosis were proposed by Hogg (1974) in order to reduce the bias of conventional estimators when the distribution is non-normal. Here we conducted a Monte Carlo simulation study to compare the performance of conventional and Hogg’s estimators, considering the most frequent continuous distributions used in health, education, and social sciences (gamma, lognormal and exponential distributions). In order to determine the bias, precision and accuracy of the skewness and kurtosis estimators for each distribution we calculated the relative bias, the coefficient of variation, and the scaled root mean square error. The effect of sample size on the estimators is also analyzed. In addition, a SAS program for calculating both conventional and Hogg’s estimators is presented. The results indicated that for the non-normal distributions investigated, the estimators of skewness and kurtosis which best reflect the shape of the distribution are Hogg’s estimators. It should also be noted that Hogg’s estimators are not as affected by sample size as are conventional estimators.


Author(s):  
Hussein Ali Sahib ◽  
Bassim Irhiem Mohammed ◽  
Ban A. Abdul Majid

Despite the unmistakable beneficial effect of clopidogrel on platelet aggregation,still there are some patient poorly responds to clopidogrel that may lead to worse cardiovascular clinical events.One hundred and twenty seven patients with cardiovascular disease (ACS,stroke,or TIA) were enrolled as a study group. Patients were recruited at coronary care unit (CCU) of Al-Yarmouk Teaching Hospital. Paletlet assessment was done by using light transmission aggregometry. between the patients that enrolled in this study there are significant inter-individual variability both skewness and Kurtosis were negative (-0.450,-0.130) respectively. 24% of patient enrolled in this study were hyporesponder.


Cancers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 2421
Author(s):  
Roberta Fusco ◽  
Vincenza Granata ◽  
Mauro Mattace Raso ◽  
Paolo Vallone ◽  
Alessandro Pasquale De Rosa ◽  
...  

Purpose. To combine blood oxygenation level dependent magnetic resonance imaging (BOLD-MRI), dynamic contrast enhanced MRI (DCE-MRI), and diffusion weighted MRI (DW-MRI) in differentiation of benign and malignant breast lesions. Methods. Thirty-seven breast lesions (11 benign and 21 malignant lesions) pathologically proven were included in this retrospective preliminary study. Pharmaco-kinetic parameters including Ktrans, kep, ve, and vp were extracted by DCE-MRI; BOLD parameters were estimated by basal signal S0 and the relaxation rate R2*; and diffusion and perfusion parameters were derived by DW-MRI (pseudo-diffusion coefficient (Dp), perfusion fraction (fp), and tissue diffusivity (Dt)). The correlation coefficient, Wilcoxon-Mann-Whitney U-test, and receiver operating characteristic (ROC) analysis were calculated and area under the ROC curve (AUC) was obtained. Moreover, pattern recognition approaches (linear discrimination analysis and decision tree) with balancing technique and leave one out cross validation approach were considered. Results. R2* and D had a significant negative correlation (−0.57). The mean value, standard deviation, Skewness and Kurtosis values of R2* did not show a statistical significance between benign and malignant lesions (p > 0.05) confirmed by the ‘poor’ diagnostic value of ROC analysis. For DW-MRI derived parameters, the univariate analysis, standard deviation of D, Skewness and Kurtosis values of D* had a significant result to discriminate benign and malignant lesions and the best result at the univariate analysis in the discrimination of benign and malignant lesions was obtained by the Skewness of D* with an AUC of 82.9% (p-value = 0.02). Significant results for the mean value of Ktrans, mean value, standard deviation value and Skewness of kep, mean value, Skewness and Kurtosis of ve were obtained and the best AUC among DCE-MRI extracted parameters was reached by the mean value of kep and was equal to 80.0%. The best diagnostic performance in the discrimination of benign and malignant lesions was obtained at the multivariate analysis considering the DCE-MRI parameters alone with an AUC = 0.91 when the balancing technique was considered. Conclusions. Our results suggest that the combined use of DCE-MRI, DW-MRI and/or BOLD-MRI does not provide a dramatic improvement compared to the use of DCE-MRI features alone, in the classification of breast lesions. However, an interesting result was the negative correlation between R2* and D.


1981 ◽  
Vol 18 (01) ◽  
pp. 76-90 ◽  
Author(s):  
Toby Lewis ◽  
J. W. Thompson

Two continuous distributions, G, H so related that any two quantiles of H are more widely separated than the corresponding quantiles of G may be said to be ‘ordered in dispersion'; Saunders and Moran have given examples. It is shown here that distributions F (called ‘dispersive' distributions) exist, e.g. the exponential, such that if G, H are ordered in dispersion then so also are the convolutions F ∗G, F ∗H. The class of dispersive distributions is determined, and shown to coincide with the class of strongly unimodal distributions.


Author(s):  
Reinaldo B. Arellano-Valle ◽  
Adelchi Azzalini

AbstractFor the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia’s measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.


2021 ◽  
Vol 95 ◽  
pp. 105110
Author(s):  
Filippos Ioannidis ◽  
Kyriaki Kosmidou ◽  
Christos Savva ◽  
Panayiotis Theodossiou

Religions ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 84
Author(s):  
Fides del Castillo ◽  
Clarence Darro del Castillo ◽  
Gregory Ching ◽  
Michael Ackert ◽  
Marie Antoinette Aliño ◽  
...  

The Centrality of Religiosity Scale (CRS) is an instrument that measures the centrality, importance, or salience of religious meanings in personality. Addressing the dearth of research on the salience of religion among Filipino Christian youths, the researchers explore in this paper the degree of religiosity of selected university students and the relevance of religious beliefs in their daily life by validating the Abrahamic forms of the Centrality of Religiosity Scale (CRS-5, CRS-10, and CRS-15). This paper specifically answers the following questions: (1) What CRS version is valid for Filipino Christian youths? (2) What is the position of the religious construct-system among selected Filipino Christian university students? and (3) How does the centrality of religiosity influences the selected Filipino Christian university students’ subjective experience and behavior? Means and standard deviations were calculated for the five subscales of the centrality of religiosity for CRS-5, CRS-10, and CRS-15. The distribution of the subscale scores was also computed using measures of skewness and kurtosis. Cronbach’s α values are provided for each of the subscales to establish internal consistency. Descriptive statistics were also computed with the use of the Statistical Package for Social Science (SPSS) software version 20. Bivariate correlations are reported for all CRS-15 items. This paper established that in a predominantly Christian country such as the Philippines, the CRS-15 is suitable in measuring the centrality of religiosity among Filipino Christian youths.


Sign in / Sign up

Export Citation Format

Share Document