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| №4, 2024: Методология и методы исследований. Модели и прогнозы |
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[RUS] / [ENG]Методология и методы исследований. Модели и прогнозы
О возможности использования эмпирической функции распределения для количественной оценки вероятности превышения нормативов по цветности
А. В. Ялалетдинова, к. т. н., доцент,
М. А. Малкова, к. х. н., доцент,
Л. В. Еникеева, к. ф-м. н., доцент,
Е. А. Кантор, д. х. н., профессор,
Уфимский государственный нефтяной технический университет,
450062, Россия, г. Уфа, ул. Космонавтов, д. 1 A. V. Yalaletdinova ORCID: 0000-0003-0883-1856,
B. M. A. Malkova ORCID: 0000-0002-3570-4062,
L. V. Enikeеva ORCID: 0000-0003-4219-4870,
E. A. Kantor ORCID: 0000-0002-9629-3324,
Ufa State Petroleum Technological University,
1, Kosmonavtov St., Ufa, Russia, 450062
e-mail
[email protected]
Аннотация
Установлено, что характер распределения значений цветности воды в рамках года зависит от сезонности, поэтому для учёта этого фактора дальнейший анализ распределения показателя произведён для каждого месяца. В качестве примера приведён анализ распределений цветности для января, мая, июля и октября. Для каждого месяца выстроены вариационные ряды и рассчитаны эмпирические функции распределения цветности воды. Выявлено, что законы распределения цветности не соответствуют нормальному и логнормальному распределениям, но достаточно точно аппроксимируются полиномами (теоретической функцией распределения). Для полученных полиномов выявлены области определения значений аргумента x, при которых они обладают всеми свойствами функции распределения (непрерывно возрастают на отрезке [0; 1]). Гипотезы о законах распределения цветности, проверенные с помощью критерия согласия Колмогорова, подтвердились. Используемая методология и полученные функции распределения цветности воды дали возможность рассчитать вероятности превышения показателем заданных значений, например, превышения норматива (20 град) для всех месяцев. Так, в январе вероятность того, что превышения норматива не произойдет, составляет 0,792, в июле 0,562, в октябре 0,809, тогда как в мае, вероятность того, что норматив по цветности не будет превышен, составляет 0,091. Знание закона распределения цветности воды, учитывающего сезонные особенности изучаемого процесса, позволяет оценить риски превышения показателем нормативных значений и использовать для принятия решений по обеспечению нормативного качества воды по показателю цветности.
Abstract
We found that the nature of the distribution of water color values within a year depends on seasonality. Therefore, to take into account the above, further analysis of the distribution of the indicator was carried out for each month. The analysis of water color distributions for January, May, July and October is given as an example. Variation series were plotted and empirical water color distribution functions were calculated for each month. It is revealed that the laws of water color distribution do not correspond to normal and log-normal distributions, but are approximated quite accurately by polynomials (theoretical distribution function). For the obtained polynomials, the domains of definition of the values of the argument x, at which they have all the properties of the distribution function (continuously increase on the interval [0; 1]) are revealed. The hypotheses about the laws of water color distribution tested using Kolmogorov–Smirnov test were confirmed. The methodology used and the resulting water color distribution functions made it possible to calculate the probabilities of an indicator exceeding the specified values, for example, exceeding the standard (20 degrees) for all months. Thus, in January, the probability of not exceeding the standard will is 0.792, in July – 0.562, in October – 0.809, while in May the probability of not exceeding the water color standard is 0.091. Knowledge of the law of water color distribution, taking into account the seasonal characteristics of the studied process, allows to assess the risks of exceeding normative values by the indicator and to use it for making decisions on ensuring normative water quality in terms of color.
Ключевые слова
качество воды, цветность воды, эмпирическая функция распределения, теоретическая функция распределения, критерий согласия Колмогорова, вероятность события
Keywords
water quality, water color, empirical distribution function, theoretical distribution function, Kolmogorov–Smirnov test, event probability
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