Aim. Traditionally, prediction of breeding values of male small horned ruminants   (rams) by referring to levels of economically useful traits of their progeny is carried  out by methods of statistical analysis. However, at the same time, there is a forecasting method based on the use of a mixed biometric model. The solution of the system  of equations constituting a mixed biometric model is associated with certain difficulties caused by the peculiarity of the system matrix. It is proposed to use integrated  mathematical packages in the forecast, by which the system of equations can be  solved in several ways, followed by analysis of the results. The prediction of progeny  values is carried out by statistical methods using three statistical tests, as well as with  the use of a mixed biometric model. It is of interest to compare estimates obtained  by using statistical methods with estimates using a mixed biometric model. Material and Methods. The initial data set was the live weight of Qigai rams, the  progeny of a group of sixteen rams belonging to eight genetic groups.   Results. It was found that the forecast of breeding values of each animal using a  mixed biometric model substantially clarifies the rank of each animal in the group  being evaluated.   Conclusion. The refinement of the estimation of breeding value is related to the  effects of the genetic groups to which the animals belong in the mixed model, as well  as the degree of relationship between them. Also the mixed model also allows one to  isolate environmental effects from the overall assessment. Solving the system of  equations in several ways will improve the reliability of the forecast.

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Приведена последовательность действий, которую необходимо выполнить селекционеру при проведении оценки племенной ценности животных. Оцениваемой группой животных являются бараны-производители. Оценка проводится по значению хозяйственно полезных признаков потомков этих производителей. В качестве таких признаков выступают живая масса потомков и их настриг шерсти. Собранные опытным путем исходные данные должны подвергнуться статистическому анализу, в ходе которого необходимо исключить аномальные измерения. Затем следует определить достоверность различий между значениями хозяйственно полезных признаков в различных генеалогических группах животных. Показано, что для определения достоверности различий необходимо провести последовательно три статистических теста. Если тест на сравнение разности двух средних с доверительными границами дает результат о случайности различий, то необходимо перейти ко второму тесту -сравнению по методу Стьюдента. Если и этот тест покажет случайный характер различий, то необходимо перейти к третьему тесту -проверке по критерию Фишера. Если хотя бы один статистический тест указывает на достоверность различий между средними показателями, то принимается гипотеза о значимом характере различий между средними значениями хозяйственно полезных признаков в исследуемых генеалогических группах. Проведен сравнительный анализ этих тестов. Показано, что наибольшей достоверностью обладает проверка статистической значимости различий по критерию Фишера. Обладая данными о неслучайности различий, можно приступить к определению гарантированного минимума превосходства одной генеалогической группы животных над другой.Ключевые слова: статистические тесты, доверительный интервал, нулевая гипотеза, альтернативная гипотеза.The article presents the sequence of actions that must be performed by the breeder when assessing the breeding value of animals. The estimated groups of animals are the tupping rams. The evaluation made on the value of the economically useful traits of the descendants from these stud rams. As economically useful traits are the live weight of offspring and of their wool clip. The baseline data collected by the experiment should undergo statistical analysis, during which anomalous measurements should be excluded. Then it is necessary to define the reliability of the differences between the values of economically useful traits in various genealogical groups of animals. The article shows that in order to determine the accuracy of the differences, it is necessary to conduct three statistical tests sequentially. If the test for comparing the difference between two averages with confidence limits gives the result of about the randomness of the differences, then it is necessary to go to the second test -comparison according to the Student's t-test. If this test also shows the random nature of the differences, then you need to go to the third test -check by Fisher criterion. If at least one statistical test indicates the reliability of the differences between the average indices then the hypothesis about the ...

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Annotation: The paper deals with the detection of wave arrival time errors in satellite navigation system by measurements conducted by stationary information system ionosphere monitoring. Develop a method of detecting the field increased ionization and the detection of the conditions for possible reduction of positioning accuracy in the presence of local ionospheric irregularities. The author examines in detail all mathematical aspects of the nature of the error; visual diagrams and graphs, as well as exhaustive mathematical calculations accompany the study. The article also discusses the process and results of computer modeling, an error that arises based on the data provided by the author, and allows one to verify the author's proposed method of detecting and predicting the occurrence of an error in determining the location. In the conclusion satity, the author speaks about the method of applying the developed method in the context of a specialized information system capable of preserving the positioning accuracy on the navigation radio signal.