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A number of soils and parent rocks at different stages of weathering were investigated for the formation of heterogeneous wettability under residual hydrophobic contamination in situ. The aim of the study was to determine specific wetting contact angles of soils and parent rocks under different conditions. The wetting contact angle was measured by the captive bubble method, which implied attaching an air bubble to the specially prepared horizontal surface of a water-placed specimen with subsequent measuring the wetting contact angle according to the profile of the bubble's photo. The soil specimens were artificially hydrophobized using media containing less than 1 wt % of oil degradation products with adapted microflora. Leached chernozem, alluvial silty loam, bentonite, dolomite–clayey marl, ornamental marl, and phyllite were studied. Based on the Pearson's goodness-of-fit criterion, good angular data approximation by both the von Mises–Tikhonov distribution and the normal distribution was found. The dependence of the types and parameters of statistical distributions of the wetting contact angle on hydrophobization conditions of the specimens was revealed. The formation of the specimens' hydrophobicity exclusively under introduced organic matter and incomplete water saturation conditions was found; at the same time, a high heterogeneity of wettability and hydrophobic areas at wetting contact angles above 129° was manifested. The results of the study can be useful for assessing and predicting the impact of soil hydrophobic contaminants and amendments, as well as for advancing methods for determining the wetting contact angle on the soil surface. [ABSTRACT FROM AUTHOR]

The paper presents a phenomenological epidemiological model for the description and prediction of the time trends of COVID-19 deaths worldwide. A bimodal distribution function—defined as the mixture of two lognormal distributions—is assumed to model the time distribution of deaths in a country. The asymmetric lognormal distribution enables better data fitting with respect to symmetric distribution functions. Besides, the presence of a second mode allows the model to also describe second waves of the epidemic. For each country, the model has six parameters, which are determined by fitting the available data through a nonlinear least-squares procedure. The fitted curves can then be extrapolated to predict the future trends of the total and daily number of deaths. Results for the six continents and the World are obtained by summing those computed for the 210 countries in the Our World in Data (OWID) dataset. To assess the accuracy of predictions, a validation study is first conducted. Then, based on data available as of 30 September 2020, the future trends are extrapolated until the end of year 2020. [ABSTRACT FROM AUTHOR]

This article proposes new symmetric and asymmetric distributions applying methods analogous as the ones in Kim (2005) and Arnold et al. (2009) to the exponentiated normal distribution studied in Durrans (1992), that we call the power-normal (PN) distribution. The proposed bimodal extension, the main focus of the paper, is called the bimodal power-normal model and is denoted byBPN(α) model, where α is the asymmetry parameter. The authors give some properties including moments and maximum likelihood estimation. Two important features of the model proposed is that its normalizing constant has closed and simple form and that the Fisher information matrix is nonsingular, guaranteeing large sample properties of the maximum likelihood estimators. Finally, simulation studies and real applications reveal that the proposed model can perform well in both situations. [ABSTRACT FROM AUTHOR]

Regression analysis is a technique widely used in different areas of human knowledge, with distinct distributions for the error term. It is the case, however, that regression models with the error term following a bimodal distribution are not common in the literature, perhaps due to the lack of simple to deal with bimodal error distributions. In this paper, we propose a simple to deal with bimodal regression model with a symmetric-asymmetric distribution for the error term for which for some values of the shape parameter it can be bimodal. This new distribution contains the normal and skew-normal as special cases. A real data application reveals that the new model can be extremely useful in such situations. [ABSTRACT FROM AUTHOR]

The influence of the number of detectors is observed by comparing a given bimodal particle size distribution (PSD) and a calculated bimodal PSD by computer simulation and experimental method. A nonlinear iteration based on the Twomey method is used for calculating PSD. An observed range of scattering angles is 5.0 × 10−4to 2.5 rad, and the Mie light scattering theory is used. The number of detectors was changed from 6 to 81 elements by the computer simulations. The algorithm of the inversion problem is applied with mean diameters of lognormal distribution in a range from 0.546 to 422 µm at a standard deviation of 0.01 and 0.27. Experimental bimodal samples are prepared by certified monodisperse polystyrene latex standards, and results are obtained by three different kinds of optics, which has 21, 41, and 81 elements detector, respectively. The polydisperse bimodal PSD converges from 42 elements of the number of detectors. The bimodal PSD of monodisperses or size range of PSD under 50 µm converges from 21 elements of the number of detectors. The accuracy of calculated PSD is effected not only by the number of detectors but also the shape of the scattering function. [ABSTRACT FROM PUBLISHER]

In order to increase the present understanding of bimodal emulsion drop size distributions, systematic series of experiments have been carried out to investigate the effects of formulation variables on bimodal drop size distributions, and probability distribution functions were proposed to analyze the distribution. The results show that, the span of the drop size and Sauter mean diameter become larger when the dispersed phase volume fraction becomes higher and rotor speed becomes lower; the Frechet function represents the experimental data satisfactorily. The prediction model of Sauter mean diameter established by combining the prediction theory of the maximum stable drop diameter and experimental analysis results can fit the experimental data well. [ABSTRACT FROM AUTHOR]

Abstract: Our aim is to explain the possible bimodality of the compositions of the magmatic rocks of the same province. In order to do so, we present a model for the crystallization of a magmatic chamber, coupling the three phenomena: solidification, sedimentation, chemical reactions between the solid and the liquid. These three phenomena make two independent dimensionless parameters appear: the ratios of the solidification rate to the transport velocity, and of the chemical kinetics to the transport velocity. The model is written for one independent chemical component. It is shown that, for certain values of the dimensionless parameters, the chemical composition of the chamber can present a bimodal distribution, starting from uniform initial conditions. This model shows that the coupling between three elementary phenomena is enough to explain the bimodality, or more generally the appearance of discontinuities of chemical compositions, without making any additional assumption. [ABSTRACT FROM AUTHOR]

Abstract: In spectral extinction particle sizing technique, an inversion method in the dependent model is proposed, in which the commonly used bimodal, mix-bimodal, and monomodal particle size distributions are retrieved using the bimodal Johnson''s S B function as the assumed type of distribution function. The feasibility and reliability of this inversion method are investigated, and the inversion using the bimodal modified beta function as the assumed type of distribution function is also discussed for comparison. Numerical simulations and experimental results indicate that the commonly used particle size distributions can be retrieved well using the bimodal Johnson''s S B function as a versatile distribution function in the dependent model with the spectral extinction data. This inversion method not only overcomes the difficulty caused by the inability to determine the type of specified distribution function accurately beforehand, but also allows the description of different types of distributions by a single model. [Copyright &y& Elsevier]

Abstract: This paper proposes a class of bilateral selection models that is associated with the centrally truncated bivariate Student- distributions. The class, especially useful for modeling inequality constrained parameter problems, is obtained from the nontruncated marginal of the centrally truncated bivariate Student- distributions. The class of distributions, possibly bimodal, strictly includes univariate Student- distribution, but with extra parameters to regulate perturbation of the symmetry. A probabilistic representation of the class is also available. Utilizing the representation, variety of properties of the class are studied and the perturbation of the symmetry is investigated in terms of skewness. These developments are followed by practical applications. [Copyright &y& Elsevier]

Over 50 years ago, in a 1955 issue of JASA, a paper on a bounded continuous distribution by Topp and Leone [C.W. Topp and F.C. Leone, A family of J-shaped frequency functions, J. Am. Stat. Assoc. 50(269) (1955), pp. 209-219] appeared (the subject was dormant for over 40 years but recently the family was resurrected). Here, we shall investigate the so-called Two-Sided Generalized Topp and Leone (TS-GTL) distributions. This family of distributions is constructed by extending the Generalized Two-Sided Power (GTSP) family to a new two-sided framework of distributions, where the first (second) branch arises from the distribution of the largest (smallest) order statistic. The TS-GTL distribution is generated from this framework by sampling from a slope (reflected slope) distribution for the first (second) branch. The resulting five-parameter TS-GTL family of distributions turns out to be flexible, encompassing the uniform, triangular, GTSP and two-sided slope distributions into a single family. In addition, the probability density functions may have bimodal shapes or admitting shapes with a jump discontinuity at the 'threshold' parameter. We will discuss some properties of the TS-GTL family and describe a maximum likelihood estimation (MLE) procedure. A numerical example of the MLE procedure is provided by means of a bimodal Galaxy M87 data set concerning V-I color indices of 80 globular clusters. A comparison with a Gaussian mixture fit is presented. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new family of symmetric-asymmetric distributions based on skew distributions and on the family of order statistics with proportional hazards. This new family of distributions is able to fit both unimodal and bimodal asymmetric data. Furthermore, it contains, as special cases, the symmetric distribution and the "skew-symmetric" family, and therefore the skew-normal distribution. Another interesting feature of the family is that the parameter controlling the distributional shape in bimodal cases takes values in the interval (0, 1); this is an advantage for computing maximum likelihood estimates of model parameters, which is performed by numerical methods. The practical utility of the proposed distribution is illustrated in two real data applications. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented. [ABSTRACT FROM AUTHOR]

The failure density function and probability density function of logarithmic lifetime are partially correlated. Normally, both patterns are either unimodal or else bimodal. This is not always the case. Quantitative criteria are introduced to check their correlation. [ABSTRACT FROM AUTHOR]

In this paper, a new family of continuous random variables with non-necessarily symmetric densities is introduced. Its density function can incorporate unimodality and bimodality features. Special attention is paid to the normal distribution which is included as a particular case. Its density function is given in closed-form which allows to easily compute probabilities, moments and other related measures such as skewness and kurtosis coefficients. Also, a stochastic representation of the family that enables us to generate random variates of this model is also presented. This new family of distributions is applied to explain the incidence of Hodgkin's disease by age. Other applications include the implications of bimodality in geoscience. Finally, the multivariate counterpart of this distribution is briefly discussed. [ABSTRACT FROM AUTHOR]