A New Truncated Muth Generated Family of Distributions with Applications

In recent years, the Muth distribution has been used for the construction of accurate statistical models, with applications in various applied fields. In this paper, we use a truncated-composed scheme to create a new unit Muth distribution, from which we motivate a more general family of continuous distributions called the truncated Muth generated family. The key benefits of this family are its analytical simplicity, connections with the exponential generated family, and flexibility conferred on any parental distribution. In particular, it improves the capability of the functions of the parental distribution, enhancing their peak, asymmetry, tail, and flatness levels, among others. The characteristics of quantile and moment measures and functions of the truncated Muth generated family are described in detail. As a concrete example, a particular distribution that extends the Weibull distribution is highlighted. In an applied part, the parameters are calculated using the maximum likelihood procedure. We use a comprehensive simulation analysis to demonstrate the accuracy of the derived estimates. The revised Weibull model is then used to fit two real-world datasets. The new model is shown to be more suited to these datasets than other competing models.

The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data

In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.

Variations in shape among observed Lyman-α spectra due to intergalactic absorption

Lyman-α (Lyα) spectra provide insights into the small-scale structure and kinematics of neutral hydrogen (HI) within galaxies as well as the ionization state of the intergalactic medium (IGM). The former defines the intrinsic spectrum of a galaxy, which, in turn, is modified by the latter. These two effects are degenerate. Using the IllustrisTNG100 simulation, we studied the impact of the IGM on Lyα spectral shapes between z ∼ 0 and 5. We computed the distribution of the expected Lyα peaks and of the peak asymmetry for different intrinsic spectra, redshifts, and large-scale environments. We find that the averaged transmission curves that are commonly applied give a misleading perception of the observed spectral properties. We show that the distributions of peak counts and asymmetry can lift the degeneracy between the intrinsic spectrum and IGM absorption. For example, we expect a significant number of triple-peaked Lyα spectra (up to 30% at z ∼ 3) if the galaxies’ HI distribution become more porous at higher redshift, as predicted by cosmological simulations. We provide a public catalog of transmission curves for simulations and observations to allow for a more realistic IGM treatment in future studies.

Applicability of a Monolithic Column for Separation of Isoquinoline Alkalodis from Chelidonium majus Extract

Isoquinoline alkaloids are the main group of secondary metabolites present in Chelidonium majus extracts, and they are still the object of interest of many researchers. Therefore, the development of methods for the investigation and separation of the alkaloids is still an important task. In this work, the application potential of a silica-based monolithic column for the separation of alkaloids was assessed. The influence of the organic modifier, temperature, salt concentration, and pH of the eluent on basic chromatographic parameters such as retention, resolution between neighboring peaks, chromatographic plate numbers, and peak asymmetry were investigated. Based on the obtained results, a gradient elution program was developed and used to separate and quantitatively determine the main alkaloids in a Chelidonium majus root extract.

Systematic Evaluation of Chromatographic Parameters for Isoquinoline Alkaloids on XB-C18 Core-Shell Column Using Different Mobile Phase Compositions

Chelidonium majusL. is a rich source of isoquinoline alkaloids with confirmed anti-inflammatory, choleretic, spasmolytic, antitumor, and antimicrobial activities. However, their chromatographic analysis is difficult because they may exist both in charged and uncharged forms and may result in the irregular peak shape and the decrease in chromatographic system efficacy. In the present work, the separation of mainC. majusalkaloids was optimized using a new-generation XB-C18 endcapped core-shell column dedicated for analysis of alkaline compounds. The influence of organic modifier concentration, addition of salts, and pH of eluents on chromatographic parameters such as retention, resolution, chromatographic plate numbers, and peak asymmetry was investigated. The results were applied to elaborate the optimal chromatographic system for simultaneous quantification of seven alkaloids from the root, herb, and fruit ofC. majus.

The real background and peak asymmetry in diffraction on nanocrystalline metals

A method to analytically calculate the column length distribution (CLD) from a single reflection of a strain-free nanocrystalline metal is proposed. It involves precise estimation of the peak background level using a physical criterion – the positivity of the CLD. The method can be applied to materials showing a dependence of the lattice constant on the crystal size, because of which the diffraction peaks display asymmetry. The analysis can provide an estimation of this dependence. Results for platinum and gold nanocrystals are presented, showing and explaining the different asymmetry of their peaks. By applying the proposed method to diffraction patterns of in situ treated gold nanocrystals, it is shown that the nanocrystal shape changes in response to changing environment.

Mapping the continuous reciprocal space intensity distribution of X-ray serial crystallography

Serial crystallography using X-ray free-electron lasers enables the collection of tens of thousands of measurements from an equal number of individual crystals, each of which can be smaller than 1 µm in size. This manuscript describes an alternative way of handling diffraction data recorded by serial femtosecond crystallography, by mapping the diffracted intensities into three-dimensional reciprocal space rather than integrating each image in two dimensions as in the classical approach. We call this procedure ‘three-dimensional merging’. This procedure retains information about asymmetry in Bragg peaks and diffracted intensities between Bragg spots. This intensity distribution can be used to extract reflection intensities for structure determination and opens up novel avenues for post-refinement, while observed intensity between Bragg peaks and peak asymmetry are of potential use in novel direct phasing strategies.