A DISTRIBUTION LAW OF THE RESULTS OF MEASUREMENT OF COMPOSITION AND PROPERTIES OF PETROLEUM PRODUCTS

Идентификацию закона распределения результатов измерений состава и свойств нефтепродуктов проводили путем проверки сложной гипотезы с использованием пяти критериев согласия: χ2-Пирсона, Колмогорова, Смирнова, ω2 Крамера-Мизеса-Смирнова; Ω2 Андерсона-Дарлинга. В качестве возможных функций распределения вероятностей рассматривали 12 симметричных одномодальных законов распределения, а также 66 смесей этих же законов распределения. Целью идентификации являлось нахождение универсального закона распределения (смеси законов распределений) справедливого для всех рассматриваемых величин. Проверка сложной гипотезы о соответствии какому-либо симметричному одномодальному закону распределения показала, что не существует универсального закона распределения справедливого для всех методик измерений состава и свойств нефтепродуктов, наиболее часто не отвергалась гипотеза о соответствии данных обобщенному логистическому распределению, распределению Лапласа и двустороннему экспоненциальному распределению. Проверка сложной гипотезы о соответствии какой-либо смеси симметричных одномодальных законов распределения показала, что эмпирическая функция распределения результатов измерений состава и свойств нефтепродуктов может быть представлена в виде смеси двух нормальных распределений с разными значениями параметров положения и масштаба. При этом для одной и той же выборки значения достигаемого уровня значимости гипотезы о соответствии смеси законов распределений в несколько раз выше среднего значения достигаемого уровня значимости гипотезы о соответствии одному закону распределения. На основе проведенного исследования обоснована вероятностная модель процесса испытаний нефтепродуктов, в рамках которой результат испытаний нефтепродуктов рассматривается как случайная величина с функцией распределения в виде смеси нормальных законов распределения: «основного» с дисперсией, не превышающей установленные требования (при статистически управляемом состоянии процесса испытаний), и «засоряющего» с дисперсией значительно превышающей установленные требования (при статистически неуправляемом состоянии процесса испытаний). The identification of a distribution law of the results of measurements of the composition and properties of petroleum products was carried out by testing a complex hypothesis using five goodness-of-fit tests: χ2-Pearson, Kolmogorov, Smirnov, ω2Cramer-Mises-Smirnov; Ω2 Anderson-Darling. Twelve symmetric unimodal distribution laws and 66 mixtures of the same distribution laws were considered as possible probability distribution functions. The purpose of the identification was to find a universal distribution law (a mixture of distribution laws) that is valid for all considered quantities. Testing the complex hypothesis of compliance with any symmetric unimodal distribution law showed that there is no universal distribution law that is valid for all measurement techniques of the composition and properties of petroleum products; most often the hypothesis of the correspondence the data to the generalized logistic distribution, the Laplace distribution and the two-sided exponential distribution was not rejected. Testing a complex hypothesis about the correspondence of any mixture of symmetric unimodal distribution laws showed that the empirical distribution function of the results of measurements of the composition and properties of petroleum products can be represented as a mixture of two normal distributions with different values ​​of the position and scale parameters. At the same time, for the same sample, the values ​​of the achieved significance level of the hypothesis about the correspondence to the mixture of distribution laws is several times higher than the average value of the achieved significance level of the hypothesis about the correspondence to one distribution law. Based on this study, a chance model of the process of testing petroleum products was substantiated, within which the result of testing petroleum products is considered as a random variable with a distribution function in the form of a mixture of normal distribution laws: "basic" with a variance not exceeding the established requirements (with a statistically controlled state of the test process), and "fouling" with a variance significantly exceeding the established requirements (with a statistically uncontrolled state of the test process).

The influence of language-specific and universal factors on acquisition of motion verbs

This study explores children’s encoding of novel verbs referring to motion events, and finds influence of both language-specific and universal constraints on meaning. Motion verbs fall into two categories—manner verbs encode how a movement happens (run, swim), and path verbs encode the starting and ending point of a motion (enter, fall). Some languages express path more frequently in the verb (Spanish, Hebrew), and others manner more frequently (English, German). Our study expands on this previous work demonstrating sensitivity to these language-specific distributions, as well as expanding to test environmental factors representing a predictable universal distribution. We find that children are sensitive to both the language-specific factors as well as the universal factors in motion verb acquisition.

Plural marking patterns of nouns and their associates in the world’s languages

Plural marking reaches most corners of languages. When a noun occurs with another linguistic element, which is called associate in this paper, plural marking on the two-component structure has four logically possible patterns: doubly unmarked, noun-marked, associate-marked and doubly marked. These four patterns do not distribute homogeneously in the world’s languages, because they are motivated by two competing motivations iconicity and economy. Some patterns are preferred over others, and this preference is consistently found in languages across the world. In other words, there exists a universal distribution of the four plural marking patterns. Furthermore, holding the view that plural marking on associates expresses plurality of nouns, I propose a hypothetical universal which uses the number of pluralized associates to predict plural marking on nouns. A data set collected from a sample of 100 languages is used to test the hypothetical universal, by employing the machine learning algorithm logistic regression.

An Algorithmic Look at Financial Volatility

In this paper, we attempt to give an algorithmic explanation to volatility clustering, one of the most exploited stylized facts in finance. Our analysis with daily data from five exchanges shows that financial volatilities follow Levin’s universal distribution Kirchherr et al. (1997) once transformed into equally proportional binary strings. Frequency ranking of binary trading weeks coincides with that of their Kolmogorov complexity estimated byDelahaye et al. (2012). According to Levin’s universal distribution, large (resp. small) volatilities are more likely to be followed by large (resp. small) ones since simple trading weeks such as “00000” or “11111” are much more frequently observed than complex ones such as “10100” or “01011”. Thus, volatility clusters may not be attributed to behavioral or micro-structural assumptions but to the complexity discrepancy between finite strings. This property of financial data could be at the origin of volatility autocorrelation, though autocorrelated volatilities simulated from Generalized Auto-Regressive Conditional Heteroskedacity (hereafter GARCH) cannot be transformed into universally distributed binary weeks.

SCALING AND MULTIFRACTALITY IN ROAD ACCIDENTAL DISTANCES

Accidental distance dynamics is investigated, based on the road accidental data of the Great Britain. The distance distribution of all the districts as an ensemble presents a power law tail, which is different from that of the individual district. A universal distribution is found for different districts, by rescaling the distribution functions of individual districts, which can be well fitted by the Weibull distribution. The male and female drivers behave similarly in the distance distribution. The multifractal characteristic is further studied for the individual district and all the districts as an ensemble, and different behaviors are also revealed between them. The accidental distances of the individual district show a weak multifractality, whereas of all the districts present a strong multifractality when taking them as an ensemble.