Theory Of Probability Statistics Research Articles

Bayesian neural networks to reduce accidents while tower crane operations

The subject of the article is methods of preventing and reducing the risk of an accident during the operation of a tower crane. The research focuses on the method when the Bayesian approach is integrated with an artificial neural network to determine probability distribution function of tower crane accident. The goal of the study isto provide the rational reasons why using a Bayesian neural network could reduce the level of accident risk while tower crane operating. To achieve the goal of the research were performed: review and analysis of the methods used in modern conditions to assess the level of accident risk when operating a tower crane; identified the reasons why these methods need improvements; proposed and provided justifications why Bayesian neural network could be a powerful method in preventing tower crane accident. During review and analysis were used: Bayes theorem, theory of probability and mathematical statistics, theory of artificial neural networks. The summary from the results of conducted analysis of modern methods which are used to estimate accident risk level for tower crane included that some methods are based on expert judgements only which are not possible to verify so the risk’s estimates obtained from those methods could be biased; other methods are good in estimation of the probability of happening of tower crane accident, however could not be used to prevent the accident to happen. In order to eliminated disadvantages of the used methods it is proposed to use Bayesian neural network to determine probability distribution function and use it to determine threshold value for risk factors which could provoke an accident’s event happens during tower crane operation.

Grain Characteristics of Perovskite Thin Films Based on SEM Image Segmentation

AbstractPerovskite solar cells (PSCs) have become the forefront and hot pot of new photovoltaic technology due to their high efficiency, low cost, and easy preparation. Understanding the microstructure characteristics of the perovskite films is one of the key factors to further improve the efficiency and stability. The characteristics of grains based on the self‐developed perovskite film morphology analysis software GrainD are studied in this article. Important perovskite film information such as the average radius of grains, the distribution pattern of grain size, the area of grain contact, and the total number of grains are obtained. The results show that the grain size distribution of the polycrystalline perovskite film follows the lognormal distribution. According to statistical probability theory and grain growth theory, the multiplication effect of multiple random factors of film growth is proposed as the reason for the lognormal distribution. This study provides an important method for analyzing the perovskite films and gives clues about the crystallization kinetics.

EVALUATION OF OPERATIONAL INDICATORS OF THE FUNCTINING OF THE TRANSPORT AND CARGO COMPLEX OF THE AGGLOMERATION FACTORY IN THE CONDITIONS OF A CHANGING ENVIRONMENT

Purpose. At the current stage of operation of the transport and cargo complex of the agglomeration factory, the processing of car flows takes place in conditions of a changing environment, which leads to low efficiency of the interaction of transport and the unloading complex. To solve this problem, it is necessary to evaluate the operational indicators of the functioning of the transport and cargo complex of the agglomeration factory, to analyze the work of the wagon transferors of the unloading complex in dynamic conditions. Research methods. The following methods were used during the research: analysis and synthesis for the study of issues and scientific publications regarding the state and ways of optimizing the functioning of the transport and cargo complex; experiment planning - to obtain a multidimensional, diverse array of statistical data; theory of probability and mathematical statistics - for data processing, obtaining correlation dependences of indicators of the functioning of the transport and cargo complex of the agglomeration factory in conditions of a variable environment. The results. The work is devoted to the solution of the scientific and technical problem of evaluating the operational indicators of the functioning of the transport and cargo complex of the agglomeration factory in the conditions of a changing environment. In the work, the level of interaction of the links of the flow process of cargo processing of the transport-cargo complex of the agglomeration factory of the base enterprise was evaluated. During the research, it was established that with the rhythmic work of the agglomeration factory and the uniform arrival of route trains with raw materials at the station, the interaction with the wagon transfer takes place in a normal mode, while the wagons are empty of the external network is close to the standard. With the complication of working conditions, especially in the period of negative temperatures when the agglomeration factory rejects raw materials, the interaction of the cargo station, the unloading complex and the defrosting garages is significantly disrupted. The idling of wagons in the specified conditions of a changing environment and especially when the wagon flow increases, the arrival reaches maximum values. Based on the evaluation of the performance indicators of the unloading complex of the agglomeration factory, it was established that the ratio of operational readiness of car transferers is at a fairly high level, the utilization rate of car transferers in terms of time is very low, and the operational technical readiness of transfer conveyors does not fully meet production requirements. The evaluation of operational indicators of the functioning of the transport-cargo complex of the agglomeration factory as a system-technical complex at the micro level made it possible to evaluate its main functions and created prerequisites for modeling the operation of the complex at the micro level in conditions of a changing environment. The scientific novelty consists in the development of a general method of evaluating the operational indicators of the functioning of the transport and cargo complex of the agglomeration factory in the conditions of a changing environment, which is based on the provisions of functional analysis. Practical significance. The presented theoretical provisions regarding the functioning of the transport-cargo complex of the agglomeration factory made it possible to evaluate the performance indicators of the unloading complex in the conditions of a changing environment, which directly affect the operation of the cargo station, and can be used in the future in models for managing flow processes in transport-cargo complexes.

Studying the impact of the angle of motor grader blade installation in the plan on its maximum force, considering the random process of occurrring difficulty in overcoming the obstacle

Problem. The operation of a motor grader takes place in different soil conditions, and individual work operations differ from each other in the patterns of external loads and form differently the load on the components of the working bodies. Goal. The goal is to determine the effect of the angle of installation of the motor grader working body (blade) on the maximum force exerted by the working body when it hits an obstacle that is difficult to overcome for different categories of soil. Methodology. In the process of studying the state of the matter, the method of analysis was used, and in theoretical studies – the analytical method, which is based on the theory of interaction of working bodies with the developed environment, as well as the provisions of the theory of reliability, probability and mathematical statistics. Results. As a result of studying the process of cutting, stopping, and hitting an obstacle, we have assessed the load of the working body. Originality. A dependence has been proposed that allows us to estimate the influence of the angle of capture of the motor grader main blade in the plan on the maximum force exerted by its working body. This takes into account the randomness of the process of appearing a difficulty to overcome an obstacle. It was found that with an increase in the angle of the blade in the plan, the maximum force on the latter increases when it encounters an obstacle. The influence of the soil category on the maximum force exerted by the working body is investigated. The maximum force reaches its highest value in the third soil category when the blade is installed directly. Practical value. It is planned to confirm the obtained dependence of the maximum force on the angle of the blade grip during real work operations by a motor grader on soils of various categories.

Study of the influence of pollution particles of 5 мkм and less on the anti-wear properties of the working fluids of hydraulic drives of construction and road machinery

Problem. An analysis of the impact of contamination of the working fluid on the state of the hydraulic equipment elements of construction and road machines, the efficiency of their operation, and also the use of the coefficient of anti-wear properties to determine the service life of working fluids is presented. The equation of the dependence of the wear rate of hydraulic equipment elements on the coefficient was obtained. Operational tests of the GR165 motor grader were also carried out, which showed that the service life of the Hydro HV 46 working fluid according to the coefficient of anti-wear properties is approximately 1184 machine hours. Methodology. In the process of studying the state of the matter, the method of analysis was used, and in theoretical studies – the analytical method, which is based on the theory of interaction of working bodies with the developed environment, as well as the provisions of the theory of reliability, probability and mathematical statistics. Results. The research results showed that coefficient Kj of anti-wear properties can be the only integral indicator of the quality of working fluids and determine their service life in hydraulic drives of Construction machines. Originality. The equation was obtained for the rate of wear, taking into account the interaction of charged particles of wear with friction surfaces. For the stationary friction mode, the equation of the balance of the contamination particles that are part of the working fluids of the hydraulic actuators and the rate of wear of friction vapor were obtained. The use of KJ coefficient as an indicator of working fluids of hydraulic drives of construction machines is presented. Practical value. The research results showed that the coefficient Kj of anti-wear properties can be the only integral indicator of the quality of working fluids and determine their service life in hydraulic drives of Construction machines.

Multi-parameter identification of concrete dam using polynomial chaos expansion and slime mould algorithm

This paper presents a novel methodology that combines polynomial chaos expansion and slime mould algorithm for multi-parameter identification of concrete dams. This methodology not only incorporates the merits of low computational cost in the polynomial chaos expansion and fast convergence of slime mould algorithm, but also considers the priori uncertainty in the input parameters by introducing statistical probability theory. By considering two examples with different complexity, this paper verifies the effectiveness of the proposed method with a univariate simply supported beam model, followed by a complex multivariate dam model to demonstrate its practicability in real engineering problems. In addition, parameter sensitivity analysis of the dam model is conducted at an extremely low cost by polynomial chaos expansion based on Sobol’ indices. Furthermore, the conventional parameter identification methods based on optimization methods directly combined with the finite element model are employed for comparison, highlighting two distinct advantages of the proposed method: (i) the proposed method improves the computational efficiency by nearly 52 times while ensuring a high accuracy, and (ii) the classical non-population optimization algorithm, Bayesian optimization, is used for comparison, revealing the outstanding performance of slime mould algorithm in terms of convergence speed and robustness. The application of the proposed algorithm is not only limited to dams, but also it can be extended to any structure.

CHARACTERISTICS OF THE IMPLICATIONS OF m-ROZPODL NAKAGAM

Detection of a correlation signal against the background of noise (occurence) is an important task of primary information processing in modern radio engineering systems of information transmission, control, navigation, radio monitoring and radiolocation. The reception of radio signals is accompanied by many accidental factors, which lead to the fact that the additive mixture very often has a non-causal distribution. For this reason, the methods of the theory of probability and mathematical statistics are used for the acceptance and processing of the accepted signal, and the acceptance and detection is regarded as a mathematical problem.
 Receiving capabilities of radio engineering systems are largely determined by the detection characteristics, which, in turn, depend on the tightness with the received signal. In order to ensure the compliance, it is necessary to know the law of distribution of the intensity and probability of the output effect of the receiver. The knowledge of the distribution of the probability of frequency determines the characteristics of the detection of the receiver of radio engineering systems and provides a wide range of functional possibilities in the execution of statistical tasks in the primary processing of information.
 Analytical expressions that determine the probability of correct detection through the probability of the hibnothreshold signal/noise ratio at the receiver output for coherent signals with a uniform initial phase and a nakagami-like amplitude are presented.
 On the basis of the obtained analytical expressions a family of curves was created for signal models, where fluctuations are very small or absent in general and which are adequately described by Nakagami’s law of dispersion.

Smart Diagnostic Expert System for Defect in Forging Process by Using Machine Learning Process

Integrating machine learning into one of the manufacturing processes, i.e., forging, is mainly concerned with making the system more intelligent by incorporating them to exhibit global understanding. Sometimes the engineer/operator can find the defects during or after the forging operation. So, the system will need some input to identify the different types of categorized defects. And also, according to that, we will develop the intelligent fault diagnosis process. We should calculate the statistical probability theory. Now, we implement the system which is the structure of the fault analysis system for the forging process. In the structure, we demonstrate the defect of the forged part, use the given imported probability to find the possible causes, and provide some remainders to reduce the fault. For enhancement of feature needs, this work includes more integration of AI with forging.

COMPUTER ORIENTED TRAININGS FOR THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS FOR FUTURE TEACHERS OF COMPUTER SCIENCE

Introduction. The problem of using computer-based teaching aids in mathematics is very relevant today, especially for future computer science teachers, that are not interested in traditional teaching methods. Since the choice of teaching methods and tools, as well as forms of organization of the educational process are closely related, the implementation of computer-based approaches to learning requires the development of appropriate methods and teaching aids. Purpose. The main purpose is a theoretical substantiation of introduction of computer-oriented means of teaching probability theory and mathematical statistics of future teachers of computer science Methods. During the research such general theoretical pedagogical methods were used as analysis of scientific and scientific-methodical literature on this issue, analysis of educational programs, curricula, textbooks and manuals; generalization and systematization, comparison, classification. Results. The use of modern computer-based tools for teaching probability theory and mathematical statistics to future teachers of computer science are considered and theoretically justified. The main types of classes using computerbased learning systems, including computer-based lectures, computer-based practical classes and laboratory-practical classes using software are considered. The use of some software tools and programming languages in the teaching of this discipline is considered and theoretically substantiated. The combination of traditional and computer forms of education allows to intensify educational and cognitive activities in the study of mathematical disciplines, including theory of probability and mathematical statistics by future teachers of computer science. Originality. The paper considers and theoretically substantiates the use of computer-based tools in the educational process in in the teaching of theory of probability and mathematical statistics by future teachers of computer science. Conclusions. The use of computer-based tools for teaching theory of probability and mathematical statistics for future computer science teachers provides a number of methodological and methodological advantages over traditional teaching, enhances cognitive activity and improves the level of practical and professional training.

Внедрение инструментов математического моделирования для анализа экономических процессов и прогнозирования затрат

The article is devoted to the consideration of various practices of using mathematical modeling for analysis of economic processes. The article contains specific examples of the application of mathematical modeling methods, including methods based on tools of the theory of probability and mathematical statistics. The purpose of the article is to draw the reader's attention to the widespread applicability and effectiveness of methods and tools of economic and mathematical modeling for solving applied problems in the subject area. The study has shown that the use of individually adapted models based on the basic elements of the mathematical apparatus is effective for solving highly specialized applied problems including tasks connected with forecasting costs and assessing possible risks.

Sublinear Random Access Generators for Preferential Attachment Graphs

We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space, and randomness complexities of such samplers. In the standard approach, the whole graph is chosen randomly according to the randomized evolving process, stored in full, and then queries on the sampled graph are answered by simply accessing the stored graph. This may require prohibitive amounts of time, space, and random bits, especially when only a small number of queries are actually issued. Instead, we propose a setting where one generates parts of the sampled graph on-the-fly, in response to queries, and therefore requires amounts of time, space, and random bits that are a function of the actual number of queries. Yet, the responses to the queries correspond to a graph sampled from the distribution in question. Within this framework, we focus on two random graph models: the Barabási-Albert Preferential Attachment model (BA-graphs) ( Science , 286 (5439):509–512) (for the special case of out-degree 1) and the random recursive tree model ( Theory of Probability and Mathematical Statistics , (51):1–28). We give on-the-fly generation algorithms for both models. With probability 1-1/poly( n ), each and every query is answered in polylog( n ) time, and the increase in space and the number of random bits consumed by any single query are both polylog( n ), where n denotes the number of vertices in the graph. Our work thus proposes a new approach for the access to huge graphs sampled from a given distribution, and our results show that, although the BA random graph model is defined by a sequential process, efficient random access to the graph’s nodes is possible. In addition to the conceptual contribution, efficient on-the-fly generation of random graphs can serve as a tool for the efficient simulation of sublinear algorithms over large BA-graphs, and the efficient estimation of their on such graphs.

Исследование характера процесса доставки партии контейнеров с тылового терминала в порт

Objective: Assessment of the need to study the process of delivering a batch of containers from the rear terminal to the port to ensure uninterrupted communication between the rear terminal and the seaport and delivery a batch of containers exactly on time. As a primary task, the problem of analyzing the factors affecting the nature of the delivery process is solved. Methods: The methods of the theory of probability and mathematical statistics were applied in terms of determining the factors that affect the nature of the delivery process. The method of constructing process models was used to create a technological model for the delivery of containers by a block train to the port. Results: A technological model of container delivery by block train is presented. Diagrams were built showing the share of the main deviations from the schedule of container trains by types of operations for traffic, traction, corporate transport services. The main factors influencing the duration of individual operations with container block trains en route and the increase in the delivery time for a batch of containers from rear terminals to the seaport as a whole are identified. The random nature of the duration of the delivery of containers by block trains following the schedule has been established. Practical importance: The need to improve the methodology for choosing a method for delivering containers from the rear terminal to the port using simulation based on the identified factors influencing individual elements of the technological model of container delivery by a block train, deviations from the delivery time of containers, scheduled running of block trains is shown.

Deterministic-Probabilistic Approach to Predict Lightning-Caused Forest Fires in Mounting Areas

Forest fires from lightnings create a tense situation in various regions of states with forested areas. It is noted that in mountainous areas this is especially important in view of the geophysical processes of lightning activity. The aim of the study is to develop a deterministic-probabilistic approach to predicting forest fire danger due to lightning activity in mountainous regions. To develop a mathematical model, the main provisions of the theory of probability and mathematical statistics, as well as the general theory of heat transfer, were used. The scientific novelty of the research is due to the complex use of probabilistic criteria and deterministic mathematical models of tree ignition by a cloud-to-ground lightning discharge. The paper presents probabilistic criteria for predicting forest fire danger, taking into account the lightning activity, meteorological data, and forest growth conditions, as well as deterministic mathematical models of ignition of deciduous and coniferous trees by electric current of a cloud-to-ground lightning discharge. The work uses synthetic data on the discharge parameters and characteristics of the forest-covered area, which correspond to the forest fire situation in the Republic of Altay and the Republic of Buryatia (Russian Federation). The dependences of the probability for occurrence of forest fires on various parameters have been obtained.

КОНЦЕПЦІЯ ПІДТРИМАННЯ ЛЬОТНОЇ ПРИДАТНОСТІ ПОВІТРЯНИХ СУДЕН НА РІЗНИХ ЕТАПАХ ЖИТТЄВОГО ЦИКЛУ

Based on the analysis of the airworthiness model of aircraft and the current legal framework in Ukraine, the fact of creating conditions for resolving most of the problems in the aviation industry is stated and further ways for the activities of regulatory bodies are determined. In the aspect of the importance of the problem of improving the system of maintaining the airworthiness of aircraft in Ukraine, the basic principles and rules for ensuring and maintaining airworthiness are determined, as well as requirements for the system for maintaining airworthiness are formulated. In the context of the formation and improvement of the aircraft continued airworthiness system, the most important requirement is to determine the composition and content of its main conceptual provisions: principles and methods to be implemented at different stages of the life cycle of aviation technology. Methods and means of ensuring and maintaining the airworthiness of aircraft follow from the tasks of the functioning of the aviation transport system and are based on the theory of reliability, probability and mathematical statistics, the theory of random processes and recovery, operations research and systems analysis, the theory of mathematical programming and experimentation, cybernetics, systems engineering and others with the use of software and computer technology. At the same time, the peculiarities of the current domestic regulatory framework, the requirements of ICAO international standards, world experience in maintaining the airworthiness of aircraft should be taken into account. In the methodological plan, when justifying the requirements for the system for ensuring and maintaining airworthiness, program-target planning and control methods can be used. The paper presents the main components of the aircraft airworthiness maintenance system. These components are responsible for various areas of its functioning in accordance with the principles and rules set out in the framework of the requirements for it. The global impact of the human factor problem on the process of maintaining and maintaining airworthiness of aircraft and on ensuring flight safety in general is shown, which is impossible without a detailed study of the features of the functioning and the corresponding improvement of the processes of maintenance and repair of aircraft.

Design and analysis of statistical probability distribution and non-parametric trend analysis for reference evapotranspiration.

Accurate estimates of reference evapotranspiration are critical for water-resource management strategies such as irrigation scheduling and operation. Therefore, knowledge of events such as spatial and temporal reference evapotranspiration (ETo) and their related principle of statistical probability theory plays a vital role in amplifying sustainable irrigation planning. Spatiotemporal statistical probability distribution and its associated trends have not yet has explored in Pakistan. In this study, we have two objectives: (1) to determine the most appropriate statistical probability distribution that better describes ETo on mean monthly and seasons wise estimates for the design of irrigation system in Khyber Pakhtunkhwa, and (2) to check the trends in ETo on a monthly, seasonal, and annual basis. To check the ETo trends, we used the modified version of the Mann-Kendall and Sen Slope. We used Bayesian Kriging for spatial interpolation and propose a practical approach to the design and study of statistical probability distributions for the irrigation system and water supplies management. Also, the scheme preeminent explains ETo, on a monthly and seasonal basis. The statistical distribution that showed the best fit ETo result occupying 58.33% and 25% performance for the design of irrigation scheme in the entire study region on the monthly level was Johnson SB and Generalized Pareto, respectively. However, according to the Anderson-Darling (AD) and Kolmogorov–Smirnov (KS) goodness of fit measure, seasonal ETo estimates were preferably suited to the Burr, Johnson SB & Generalized Extreme Value. More research work must be conduct to assess the significance of this study to other fields. In conclusion, these findings might be helpful for water resource management and policymaker in future operations.

Algorithm for determining the conductive low-frequency electromagnetic interference in electrical networks

The electric power systems (EES) of various industrial enterprises for a number of reasons are characterized by low quality of electric energy, in particular, the presence of higher harmonics in the networks, as a result of which conductive low-frequency electromagnetic interference (EMF) occurs. This leads to the problem of the quality of electric energy in the EPS, which negatively affects the electrical equipment. The problem is vast and the question of solving various problems, one of which is the determination of conductive low-frequency electromagnetic fields by the coefficient of the nth harmonic component of the voltage, is not solved. Development of an algorithm for determining the conductive low-frequency EMF by the coefficient of the nth harmonic component of the voltage. This algorithm allows scientifically sound assessment of the electromagnetic environment in electrical networks. Creating a sequence of decisions to determine the quality criterion for the functioning of electric power systems by the coefficient of the nth harmonic component of the voltage. Based on the theory of probability and mathematical statistics, an algorithm has been developed for determining the conductive low-frequency electromagnetic field by the coefficient of the nth harmonic component of the voltage. The developed algorithm is based on the requirements of the international state standard GOST 32144-2013. Using this algorithm, a computer program has been developed that allows the automated calculation of the parameters of the electromagnetic environment (distribution parameters, the probability of their occurrence). Moreover, it makes an automated calculation of such distribution parameters of the values of the coefficient of the nth harmonic component of the voltage as the mean value and standard deviation. Also, the program performs an automated calculation of the probability of the coefficients of the nth harmonic component of the voltage exceeding the normalized values and the probability of the appearance of the conductive low-frequency EMF by the coefficient of the nth harmonic component of the voltage during the calculation period. In turn, it is also able to visualize the data arrays that were obtained in the course of various experimental studies using an oscillogram and a histogram.

ДИСЦИПЛИНА «ПРАВОВАЯ СТАТИСТИКА» КАК СРЕДСТВО ПОДГОТОВКИ ВЫПУСКНИКОВ ВУЗОВ МВД РОССИИ К ИСПОЛЬЗОВАНИЮ МАТЕМАТИЧЕСКИХ МЕТОДОВ В ИНФОРМАЦИОННО-АНАЛИТИЧЕСКОЙ РАБОТЕ

Statement of the problem. The relevance of the study is due to the fact that at present the activities of law enforcement agencies are based on the introduction of a unified system of information and analytical support of the RF Interior Ministry. The effective use of digital technologies depends on the quality of training of legal professionals, in terms of development of their basic knowledge, skills and abilities in the field of computational and analytical activities as the basis for professional thinking development. The purpose of the article is to justify the need to include the basics of the general theory of statistics, probability theory and mathematical statistics in the course of Legal Statistics as a basis and tool for analyzing socio-economic phenomena closely related to the activities of anti-crime law enforcement agencies following the historical and pedagogical analysis of applying statistics in jurisprudence. The research methodology consists of the analysis and synthesis of regulatory documents in the field of higher education (including educational standards of different generations in the areas of legal training implemented in the RF Interior Ministry universities), the history of teaching the course in Legal Statistics, as well as scientific and pedagogical literature. Research results. The study shows that the content of the course in Legal Statistics for students in legal specialization should include not only branch norms, but also the basics of the theory of probability and mathematical statistics. The fundamental nature of mathematical training helps to develop the basic grounds of professional thinking among specialists of the Russian law enforcement system. Conclusions. The study methodology made it possible to clarify the need for teaching mathematical fundamentals (including the elements of the theory of probability and mathematical statistics) while teaching Legal Statistics. This contributes to a higher level of professional competence among RF Interior Ministry graduates of higher educational institutions, their readiness to apply mathematical calculations in analytical activities.

Государственные заимствования и их влияние на рост общественного благосостояния

The article is devoted to the study of the role of government borrowing in the system of modern market relations, in which the search for tools to maintain or increase the social welfare of citizens is one of the urgent issues. In conditions of weak economic growth and a slow increase in the standard of living of the population, one of the most significant ways to activate economic growth is precisely the amount of funds raised by the state for solving key social problems. As part of the study, an analysis of internal and external government borrowings of the Russian economic system was carried out, using the tools of the theory of probability and mathematical statistics, the degree of influence of government debt on macroeconomic development was revealed, and ways to optimize government borrowing were proposed.

Asymptotically Normal Estimators for the Parameters of the Gamma-Exponential Distribution

Currently, much research attention has focused on generalizations of known mathematical objects in order to obtain adequate models describing real phenomena. An important role in the applied theory of probability and mathematical statistics is the gamma class of distributions, which has proven to be a convenient and effective tool for modeling many real processes. The gamma class is quite wide and includes distributions that have useful properties such as, for example, infinite divisibility and stability, which makes it possible to use distributions from this class as asymptotic approximations in various limit theorems. One of the most important tasks of applied statistics is to obtain estimates of the parameters of the model distribution from the available real data. In this paper, we consider the gamma-exponential distribution, which is a generalization of the distributions from the gamma class. Estimators for some parameters of this distribution are given, and the asymptotic normality of these estimators is proven. When obtaining the estimates, a modified method of moments was used, based on logarithmic moments calculated on the basis of the Mellin transform for the generalized gamma distribution. On the basis of the results obtained, asymptotic confidence intervals for the estimated parameters are constructed. The results of this work can be used in the study of probabilistic models based on continuous distributions with an unbounded non-negative support.

Application of a randomized response technique for the sensitive question survey in female sex workers in Xichang, China.

The technique of sampling is a particularly important aspect of sampling surveys, and the method of determining sample size is the key link in sampling technique. However, a sample size determination method for complex sampling surveys of sensitive issues using a randomized response model is not yet available. In this work, we drew from the theory of probability and mathematical statistics, and developed a series of formulas for sample size determination that are required to estimate the overall proportion and mean on dichotomous sensitive questions in 3-stage sampling using Simmons models. Shortly after generating the formulas, we successfully applied them to a pre-survey regarding sensitive issues among female sex workers (FSWs) in Xichang, and found their practical application to achieve satisfactory effects. By using a large number of Monte Carlo simulation sampling tests, the reliability of the survey methods and formulas for sensitive question surveys were found to be high, but the randomized response technique (RRT) cannot completely eliminate the possibility of social acceptability bias. RRT is an acceptable method for sensitive question surveys within sensitive populations, and this new sampling method is liable to be used for sensitive question surveys of large populations. We believe that the results obtained in the field of public health can provide some data support for clinical practice.