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In this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-associated dependency framework. We consider the non parametric estimation of the conditional distribution function by the kernel method in the presence of the quasi-associated dependence, and we establish under general hypotheses the almost complete convergence with speed of the estimator built in the associated case. The estimation of the conditional hazard function will be conducted by utilizing the two outcomes of the conditional distribution function and the conditional density. We establish the asymptotic normality of the kernel estimator as the conditional risk function of a properly normalized functional. We explicitly give the asymptotic variance. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data. All the statistical analyses were performed using R software. [ABSTRACT FROM AUTHOR]

Ceramic grinding, which in this paper is defined as a method of using ceramic materials as grinding media, is favored by many processing plants as an emerging high-efficiency and energy-saving grinding method. This paper investigates the effect of slurry mass concentration on the grinding characteristics of magnetite by taking the feed of the secondary ball mill for processing magnetite as the research object. The study results show that the slurry mass concentration significantly affects the ceramic ball grinding characteristics of magnetite, especially for coarse particles. When the grinding concentration is higher than 50%, the breakage rate of magnetite plummets to 1/3 of the value at low mass concentrations. The standard deviation of the breakage rate relative to the concentration gradually decreases as the feed size falls, indicating that the coarser the feed size, the more sensitive the ceramic ball grinding is to the concentration, and thus industrial secondary ceramic ball mills need to avoid grinding under high-quality concentrations. The change in the consistency parameter of distribution function and zero-order output characteristics signals a radical variation in the grinding characteristics of magnetite using the ceramic ball grinding method compared to conventional grinding. Because the ceramic ball grinding method can greatly reduce energy consumption while lowering the chance of overgrinding, this grinding method deserves more attention as the world works to reach carbon neutrality and emissions peak. [ABSTRACT FROM AUTHOR]

The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters; hence, the problem is greatly simplified since it is reduced to the search for an extremum of some function. [ABSTRACT FROM AUTHOR]

This paper suggests new estimators for cumulative distribution function (CDF) using L ranked set sampling (LRSS) and robust extreme ranked set sampling (RERSS) methods. The proposed estimators are deduced based on maximum likelihood estimation method and its asymptotic properties are theoretically investigated. Comparison study has been made to demonstrate the efficiency of the proposed estimators. It is found that when the data contain outliers, the proposed estimators are less sensitive and have a satisfied behavior compared to their analog in ranked set sampling as the population CDF is far away from the boundaries. Motivated by this efficiency gain, we provided new estimators for system reliability R = P (Y > X) using LRSS and RERSS. Through a Monte Carlo simulation study, the performance of the introduced reliability estimators is also examined. A real data set is analyzed to illustrate the applicability of the proposed various estimators. [ABSTRACT FROM AUTHOR]

This article deals with the analysis of the multi-cell association setup, and it exploits the possibility of enhancing coverage in the envisioned sixth generation (6G) large-scale cellular networks. Specifically, we propose a simple, effective approach for finding a closed-form solution to the coverage probability of a given user in a multi-cell association regime of downlink multiple-user multiple-input multiple-output (MU-MIMO) systems. In particular, a Rayleigh fading channel is considered, wherein the transmitter has only the knowledge of the second-order statistics of the channel. The proposed work uses an indefinite quadratic formulation method and thereby investigates the effect of cell association in a correlated downlink broadcast channel with co-channel interference, additive white noise, and multiple transceiver antenna elements. In the results, we show that a predefined signal-to-interference-plus-noise ratio (SINR) threshold dictates an effective multi-cell association setup, and we identify the region in which a multi-cell association performs better that a single association-based network. The derived theoretical expressions in this paper are validated by the same means of simulation. [ABSTRACT FROM AUTHOR]

The present paper addresses computational and numerical challenges when working with t copulas and their more complicated extensions, the grouped t and skew t copulas. We demonstrate how the R package nvmix can be used to work with these copulas. In particular, we discuss (quasi-)random sampling and fitting. We highlight the difficulties arising from using more complicated models, such as the lack of availability of a joint density function or the lack of an analytical form of the marginal quantile functions, and give possible solutions along with future research ideas. [ABSTRACT FROM AUTHOR]