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- W202348227 abstract "This chapter discusses the basic properties of distributions. It explains mean value, variance, median, and other moments. The mean value is the simplest parameter that characterizes a distribution. In probability theory and, particularly, in the theory of statistics, many other parameters are used to describe certain features of a distribution. The chapter describes the median that may be defined as any root of the equation P(x) = 12. If one thinks of the distribution as a mass distribution, the next concept of interest is a quantity significant of the degree of concentration of the mass around its centroid. It is usually defined as a measure of concentration, a quantity called the variance that is in close analogy to the moment of inertia. If the mean value and variance of a distribution are known, the distribution is by no means determined. In connection with mean value and variance, the chapter also describes Tchebycheff's inequality and its generalizations. The great importance of Tchebycheff's inequality lies in its universal validity. For this very reason, it rarely provides the sharpest results in individual cases. It serves as an important tool in proofs and general estimates. A wide generalization of Tchebycheff's inequality is because of Kolmogorov and is known as Kolmogorov's inequality. The chapter also discusses Kolmogorov's inequality." @default.
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- W202348227 date "1964-01-01" @default.
- W202348227 modified "2023-10-18" @default.
- W202348227 title "BASIC PROPERTIES OF DISTRIBUTIONS" @default.
- W202348227 doi "https://doi.org/10.1016/b978-1-4832-3213-3.50006-3" @default.
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