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The log-normal distribution (skewed distribution or asymmetry distribution) is used to describe random variables comprising positive real values. It is well known that the logarithm values of these are normally distributed (symmetry distribution). Positively right-skewed data applicable to the log-normal distribution are frequently observed in the fields of environmental studies, biology, and medicine. The number of zero observations follows a binomial distribution. However, problems can arise in the analysis of data containing zero observations along with log-normally distributed data, for which the delta-lognormal distribution is often referred to for using the analysis of the data. In statistics, the percentile provides the relative standing of a numerical data point when compared to all of the others in a distribution with reference to the observations at or below it. In this study, estimates for the confidence interval for the ratio of the percentiles of two delta-lognormal distributions are constructed using fiducial generalized confidence interval approaches based on the fiducial quantity and the optimal generalized fiducial quantity, the Bayesian approach, and the parametric bootstrap method. As assessed by Monte Carlo simulations using the RStudio programming in terms of the coverage probability and the average length, the Bayesian approach performed quite well by providing adequate coverage probabilities along with the shortest average lengths in all of the scenarios tested. Daily rainfall data contain both zero and positive values. The daily rainfall data can usually be fitted to the delta-lognormal distribution. Their application to rainfall data is also provided to illustrate their efficacies with real data. The efficacy of the approach is used to compare two rainfall dispersion populations. [ABSTRACT FROM AUTHOR]

The log-normal distribution (skewed distribution or asymmetry distribution) is used to describe random variables comprising positive real values. It is well known that the logarithm values of these are normally distributed (symmetry distribution). Positively right-skewed data applicable to the log-normal distribution are frequently observed in the fields of environmental studies, biology, and medicine. The number of zero observations follows a binomial distribution. However, problems can arise in the analysis of data containing zero observations along with log-normally distributed data, for which the delta-lognormal distribution is often referred to for using the analysis of the data. In statistics, the percentile provides the relative standing of a numerical data point when compared to all of the others in a distribution with reference to the observations at or below it. In this study, estimates for the confidence interval for the ratio of the percentiles of two delta-lognormal distributions are constructed using fiducial generalized confidence interval approaches based on the fiducial quantity and the optimal generalized fiducial quantity, the Bayesian approach, and the parametric bootstrap method. As assessed by Monte Carlo simulations using the RStudio programming in terms of the coverage probability and the average length, the Bayesian approach performed quite well by providing adequate coverage probabilities along with the shortest average lengths in all of the scenarios tested. Daily rainfall data contain both zero and positive values. The daily rainfall data can usually be fitted to the delta-lognormal distribution. Their application to rainfall data is also provided to illustrate their efficacies with real data. The efficacy of the approach is used to compare two rainfall dispersion populations.

Highlights • The kinematic properties of movements being generated unimanually and bimanually were compared. • Parameters estimated using the Delta- and Sigma-Lognormal model were analyzed in addition to kinematic variables. • Bimanual Movements result in an overall delayed, slower, and less efficient movements. • The findings were overall similar when using the Delta- and Sigma-lognormal model. • The Sigma-lognormal model suggested additionally that the two hands contribute differently to the manual conditions. Abstract The use of large digitizers, allowing users to interact using both hands simultaneously, are getting more and more popular in applications requiring human computer interaction. In most of these applications, gesture commands are used and these commands to activate specific actions can provide also information about the neuromuscular system of the user. As shown for single hand interactions, understanding of the neuromotor coordination processes using both hands could improve interface design. In the present paper, we address this topic with a first study aimed to characterize the bimanual and unimanual coordination. We compare the kinematic properties of movements performed unimanually and bimanually. Rapidly drawn lines are assessed using kinematic features in addition to the parameters estimated by two models, i.e., the Delta-Lognormal model and Sigma-Lognormal model. Sixteen right-handed participants were instructed to conduct 120 rapid drawing actions with the dominant hand, non-dominant hand, and both hands simultaneously. Kinematic variables (i.e. reaction time (RT) and movement time (MT)) together with parameters of the Delta-Lognormal model and Sigma-Lognormal model were extracted from the movements. The latter parameters estimate the agonist and antagonist synergies that contribute to the overall movement production of the rapid drawn lines. A 2 × 2 repeated measures ANOVA was applied to all dependent variables with manual condition (uni- vs bimanual) and hand used (dominant vs non-dominant) as independent factors. Parameters of the Delta-Lognormal model and Sigma-Lognormal model revealed that the prolonged preparation time of the bimanual task had both a central and peripheral origin, i.e., it originated at the CNS and neuromuscular levels. Furthermore, findings from the Sigma-lognormal model suggested that the dominant and non-dominant hand contribute differently to the manual conditions, which may lead to new heuristics for implementing command systems for computer interaction systems requiring bimanual manipulation as well as designing automatic systems for rehabilitative training. [ABSTRACT FROM AUTHOR]

The problems of estimating the mean and an upper percentile of a lognormal population with nonnegative values are considered. For estimating the mean of a such population based on data that include zeros, a simple confidence interval (CI) that is obtained by modifying Tian's [Inferences on the mean of zero-inflated lognormal data: the generalized variable approach. Stat Med. 2005;24:3223—3232] generalized CI, is proposed. A fiducial upper confidence limit (UCL) and a closed-form approximate UCL for an upper percentile are developed. Our simulation studies indicate that the proposed methods are very satisfactory in terms of coverage probability and precision, and better than existing methods for maintaining balanced tail error rates. The proposed CI and the UCL are simple and easy to calculate. All the methods considered are illustrated using samples of data involving airborne chlorine concentrations and data on diagnostic test costs. [ABSTRACT FROM AUTHOR]

Abstract: The study of rapid strokes is a direct or indirect prerequisite in many fundamental research projects, as well as in the design of many practical applications dealing with handwriting. This paper outlines a family of models, derived from the Kinematic Theory of Human Movements. It explains how the nested models in this family can be used coherently, in the context of a multi-level representation paradigm, to analyze both the trajectory and the velocity of strokes with a progressive amount of detail. In the context of a comprehensive survey of previously published work, this paper highlights many new features of stroke production, when the vectorial version of the theory is fully exploited. In this perspective, the Kinematic Theory is depicted as a potential tool to facilitate communications among researchers working in the multi-disciplinary field of Graphonomics. [Copyright &y& Elsevier]