Goodness-of-fit Measures Based on the Mellin Transform for Beta Generalized Lifetime Data

In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient goodness-of-fit (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fr\’{e}chet and Kumaraswamy distributions; and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fr\’{e}chet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling’s $T^2$ statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

Evenness-Richness Scatter Plots: a Visual and Insightful Representation of Shannon Entropy Measurements for Ecological Community Analysis

ABSTRACT Shannon’s entropy is a popular alpha diversity metric because it estimates both richness and evenness in a single equation. However, since its value is dependent on both those parameters, there is theoretically an infinite number of richness/evenness value combinations translating into the same index score. By decoupling both components measured by Shannon’s entropy, two communities having identical indices can be differentiated by mapping richness and evenness coordinates on a scatter plot. In such graphs, confidence ellipses would allow testing significant differences between groups of samples. Multivariate statistical tests such as permutational multivariate analysis of variance (PERMANOVA) can be performed on distance matrices calculated from richness and evenness coordinates and detect statistically significant differences that would have remained unforeseen otherwise. Therefore, plotting richness and evenness on two-dimensional (2D) graphs gives a more thorough understanding of how alpha diversity differs between groups of samples.

Evenness-richness scatter plots: a graphical, intuitive approach to alpha diversity analysis

Shannon’s diversity index is a popular alpha diversity metric because it estimates both richness and evenness in a single equation. However, since its value is dependent of both those parameters, there is theoretically an infinite number of richness / evenness value combinations translating into the same index score. By decoupling both components measured by Shannon’s index, two communities having identical indices can be differentiated by mapping richness and evenness coordinates on a scatter plot. In such graphs, confidence ellipses would allow testing significant differences between groups of samples. Multivariate statistical tests such as PERMANOVA can be performed on distance matrices calculated from richness and evenness coordinates and detect statistically significant differences that would have remained unforeseen otherwise.

Evaluation of Discrimination Performance in Case for Multiple Non-Discriminated Samples: Classification of Honeys by Fluorescent Fingerprinting

In this study we develop a variant of fluorescent sensor array technique based on addition of fluorophores to samples. A correct choice of fluorophores is critical for the successful application of the technique, which calls for the necessity of comparing different discrimination protocols. We used 36 honey samples from different sources to which various fluorophores were added (tris-(2,2′-bipyridyl) dichlororuthenium(II) (Ru(bpy)32+), zinc(II) 8-hydroxyquinoline-5-sulfonate (8-Ox-Zn), and thiazole orange in the presence of two types of deoxyribonucleic acid). The fluorescence spectra were obtained within 400–600 nm and treated by principal component analysis (PCA). No fluorophore allowed for the discrimination of all samples. To evaluate the discrimination performance of fluorophores, we introduced crossing number (CrN) calculated as the number of mutual intersections of confidence ellipses in the PCA scores plots, and relative position (RP) characterized by the pairwise mutual location of group centers and their most distant points. CrN and RP parameters correlated with each other, with total sensitivity (TS) calculated by Mahalanobis distances, and with the overall rating based on all metrics, with coefficients of correlation over 0.7. Most of the considered parameters gave the first place in the discrimination performance to Ru(bpy)32+ fluorophore.

BIOELECTRICAL VECTOR ANALYSIS IN OBESE ADOLESCENTS

ABSTRACT Objective: To evaluate the hydration of obese and non-obese adolescents by vectorial bioimpedance analysis, in addition to verifying the associations between obesity and bioelectrical impedance vectorial analysis (BIVA) parameters. Methods: A cross-sectional study with adolescents between 14 and 18 years old (n=489, 300 boys and 189 girls). Electric bioimpedance (BIA; Quantum_II, RJL system, Rome, Italy) provided resistance and reactance parameters to calculate phase angle (PA), fat-free mass (FFM) and body fat (%BF). The confidence ellipses were compared, and the construction of the tolerance ellipses allowed individual and qualitative evaluation of the vectors and classification in dehydrated, normohydrated and hyperhydrated. Results: 78 obese and 411 eutrophic adolescents participated. Resistance (p<0.001) and reactance (p<0.001) and their normalization by stature (p<0.001) were reduced in the obese, whereas the PA was higher (p=0.003). %BF was 11.3% higher in obese adolescents. The main vector of the obese, both male (D=1.38; p<0.001) and female (D=1.49; p<0.001), indicated greater hydration. The ellipse of tolerance of the total sample showed that 25 (32.1%) were hyperhydrated and 02 (2.6%) vectors positioned in the sense of dehydration. A total of 17 (53.2%) girls and 16 (34.8%) boys were hyperhydrated. Logistic regression showed an inverse relation of BMI with resistance (p<0.001), reactance (p<0.001) and both normalized by stature. Adolescents with increased PA (p<0.001) were twice as likely to present obesity. Conclusions: Obese adolescents were hyperhydrated and there was an inverse relationship of BMI with resistance and direct with PA.

Acceptability of oral liquid pharmaceutical products in older adults: palatability and swallowability issues

Background In institutional care, oral liquid pharmaceutical products are widely prescribed for older patients, especially for those with swallowing disorders. As medicines acceptability is a key factor for compliance in the older population, this study investigated the acceptability of oral liquid pharmaceutical products in this targeted population. Methods An observational, multicenter, prospective study was conducted in eight geriatric hospitals and eight nursing homes in France. Observers reported several behaviours/events describing the many aspects of acceptability for various pharmaceutical products’ uses in patients aged 65 and older. Acceptability scores of oral liquid pharmaceutical products were obtained using an acceptability reference framework (CAST - ClinSearch Acceptability Score Test®): a 3D-map summarizing the different users’ behaviors, with two clusters defining the positively and negatively accepted profiles materialized by the green and red zones, respectively. Results Among 1288 patients included in the core study and supporting the acceptability reference framework, 340 assessments were related to the administration of an oral liquid pharmaceutical product. The mean age of these patients was 87 (Range [66-104y]; SD = 6.7), 68% were women and 16% had swallowing disorders. Globally, the oral liquid pharmaceutical products were classified as “positively accepted,” the barycenter of the 340 assessments, along with the entire confidence ellipses surrounding it, were positioned on the green zone of the map. Sub-populations presenting a different acceptability profile have also been identified. For patients with swallowing disorders, the oral liquid pharmaceutical products were classified as “negatively accepted,” the barycenter of the 53 assessments along with 87% of its confidence ellipses were associated with this profile. A gender difference was observed for unflavored oral liquids. In women, they were classified “negatively accepted,” the barycenter of the 68 assessments with 75% of its confidence ellipses were located in the red zone, while they were classified “positively accepted” in men. Conclusion This study showed that oral liquid pharmaceutical products are a suboptimal alternative to solid oral dosage forms in patients with swallowing disorders. To ensure an optimal acceptability, prescribers should also consider the presence of a taste-masker in these oral liquids. As highlighted herein, palatability remains crucial in older populations, especially for women.

A new method for absolute underground positioning based on transient electromagnetics

SUMMARY We present a procedure for localizing underground positions using a time-domain inductive electromagnetic (EM) method. The position to be localized is associated with an EM receiver placed inside the Earth. An EM field is generated by one or more transmitters located at known positions at the Earth’s surface. We then invert the EM field data for the receiver positions using a trust-region algorithm. For any given time regime and source–receiver geometry, the propagation of the electromagnetic fields is determined by the electrical conductivity distribution within the Earth. We show that it is sufficient to use a simple 1-D model to recover the receiver positions with reasonable accuracy. Generally, we demonstrate the robustness of the presented approach. Using confidence ellipses and confidence intervals we assess the accuracy of the recovered location data. The proposed method has been extensively tested against synthetic data obtained by numerical experiments. Furthermore, we have successfully carried out a location recovery using field data. The field data were recorded within a borehole in Alberta (Canada) at 101.4 m depth. The recovered location of the borehole receiver differs from the actual location by 0.70 m in the horizontal plane and by 0.82 m in depth.