Sine Topp-Leone-G family of distributions: Theory and applications

Recent studies have highlighted the statistical relevance and applicability of trigonometric distributions for the modeling of various phenomena. This paper contributes to the subject by investigating a new trigonometric family of distributions defined from the alliance of the families known as sine-G and Topp-Leone generated (TL-G), inspiring the name of sine TL-G family. The characteristics of this new family are studied through analytical, graphical and numerical approaches. Stochastic ordering and equivalence results, determination of the mode(s), some expansions of distributional functions, expressions of the quantile function and moments and basics on order statistics are discussed. In addition, we emphasize the fact that the sine TL-G family is able to generate original, simple and pliant trigonometric models for statistical purposes, beyond the capacity of the former sine-G models and other top models of the literature. This fact is revealed with the special three-parameter sine TL-G model based on the inverse Lomax model, through an efficient parametric estimation and the adjustment of two data sets of interest

The Transmuted Muth Generated Class of Distributions with Applications

Recently, the Muth generated class of distributions has been shown to be useful for diverse statistical purposes. Here, we make some contributions to this class by first discussing new theoretical facts and then introducing a natural extension of it via the transmuted scheme. The extended class is described in detail, emphasizing the characteristics of its probability and reliability functions, as well as its moments. Among other things, we show that it can extend the possible values of the mean and variance of the parental distribution, while maintaining symmetry or creating various types of asymmetry. The mathematical inference of the parameters is also discussed. Special attention is paid to the distribution of the new class using the log-logistic distribution as a parent. In an applied work, we evaluate the behavior of the corresponding model by using simulated and practical data. In particular, we employ it to fit two real-life data sets, one with environmental data and the other with survival data. Standard statistical criteria validate the importance of the proposed model

Box-Cox Gamma-G Family of Distributions: Theory and Applications

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Ristić–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models

Estimation of different types of entropies for the Kumaraswamy distribution.

The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided

The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions

Assessment of oxidative stability and physicochemical, microbiological, and sensory properties of beef patties formulated with baobab seed (Adansonia digitata) extract

The present study was conducted to evaluate the oxidative stability and the physicochemical, microbiological, and sensory properties of beef patties formulated with different concentrations (1%, 2%, and 3%) of baobab seed extract (BSE) during storage at 4 °C. The BSE contained a considerable number of phenolic compounds and exhibited antioxidant and antimicrobial activities (both on gram-positive and negative bacteria). The chemical composition of the patties was not altered by BSE treatment. However, the addition of 2% and 3% BSE improved the lipid stability and enhanced the antioxidant activity of beef patties during storage. Furthermore, the shelf-life of patties formulated with 2% and 3% of BSE increased from 7 days (control group) to 21 days. Moreover, the patties formulated with BSE received overall acceptability in the sensory evaluation. In conclusion, the inclusion of 2% or 3% BSE could be recommended as a natural antioxidant additive in beef patties