Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves

A Lorenz curve is a graphical representation of the distribution of income or wealth within a population. The generalized Lorenz curve can be created by scaling the values on the vertical axis of a Lorenz curve by the average output of the distribution. In this thesis, we propose two nonparametric methods for testing the equality of two generalized Lorenz curves. Both methods are based on empirical likelihood and utilize a U -statistic. We derive the limiting distribution of the likelihood ratio, which is shown to follow a chi-squared distribution with one degree of freedom. We conduct simulations to compare the proposed methods and an existing method by examining Type I error rates and power across various sample sizes and distribution assumptions. Our results show that the proposed methods exhibit superior performance in finite samples, particularly in small sample sizes, and are robust across various scenarios. Finally, we use real-world data to illustrate the methods of testing two generalized Lorenz curves

Schemes Of Solid-phase Spectrophotometric Analysis Of Food Objects

The aim of research is development of approaches to the development of schemes for microelement analysis of food objects. This will make it possible to monitor food quality by simple and affordable methods in factory laboratories.Based on data on the immobilization of dyes on ion exchangers and on the interaction of metal ions or their complexes with immobilized dyes, solid-phase spectrophotometric (SPS) and photometric methods for determining metal ions in food technology, biotechnology and the environment have been developed.Techniques are sensitive. High distribution coefficients (D³104 cm3/g) of metal ions help to reduce the detection limit when using immobilized dye as compared to the reaction in solution. Based on the detection limit values (DLV), the proposed sorption-spectrophotometric methods for determining metal ions are second only to the atomic absorption (AAS) determination of Cd (II) and Hg (II) ions and the polarographic determination of Cd (II) ions. However, the proposed methods for the determination of these metal ions are sufficient for the determination of Cd (II) and Hg (II) ions in food products at the MPC level. In the case of determination of Pb (II), Zn (II), Cu (II), Fe (III) ions, the developed methods have advantages over standard methods for determination of metal ions in food products, since they make it possible to determine these ions at a level ≤0.1…0.5 MPC;Ion exchangers with immobilized dyes and solid-phase spectrophotometric determination methods with their participation are environmentally safe, since they do not require the use of toxic organic reagents; are simple in execution and economically advantageous because of the low cost of used materials and reagents.The correctness of the results of the determination by the developed methods is proved: by comparison with the results of determinations on standard methods at various analysis objects using the method of additives, standard samples. The relative standard deviation of the developed SPS determination procedures does not exceed 0.10, which indicates satisfactory reproducibility of the results. The developed methods exceed the majority of standard and best analogs, known from the literature, for sensitivity and selectivity. The used methods of analysis are characterized by the simplicity of the experiment, ecological safety, do not require special expensive equipment, highly qualified personnel and a stationary laboratory