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Title:
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Статистичні розподіли хі-квадрат, Стьюдента, Фішера – Снедекора та їх застосування |
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Author:
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Моцний, Ф. В.
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Abstract:
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Моцний Ф. В. Статистичні розподіли хі-квадрат, Стьюдента, Фішера – Снедекора та їх застосування // Статистика України. 2018. №1. С. 16–23. |
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Description:
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У роботі з єдиної позиції проаналізовані статистичні розподіли випадкових величин хі-квадрат, Стьюдента і Фішера – Снедекора З’ясовані особливості застосування цих розподілів для перевірки відповідності емпіричних розподілів вибірки теоретично передбачуваним генеральної сукупності Розглянуті числові характеристики і наведені формули для їх розрахунків Узагальнені результати теоретичних і прикладних досліджень. The Chi-square distribution is the distribution of the sum of squared standard normal deviates The degree
of freedom of the distribution is equal to the number of standard normal deviates being summed For the first
time this distribution was studied by astronomer F Helmert in connection with Gaussian low of errors in 1876 Later K Pearson named this function by Chi-square Therefore Chi –square distribution bears a name
of Pearson’s distribution
The Student's t-distribution is any member of a family of continuous probability distributions that arises
when estimating the mean of a normally distributed population in situations where the sample size is small and
population standard deviation is unknown It was developed by W Gosset in 1908
The Fisher–Snedecor distribution or F-distribution is the ratio of two-chi-squared variates The
F-distribution provides a basis for comparing the ratios of subsetsof these variances associated with different
factors The Fisher-distribution in the analysis of variance is connected with the name of R Fisher (1924),
although Fisher himself used quantity for the dispersion proportion
The Chi-square, Student and Fisher – Snedecor statistical distributions are connected enough tight with
normal one Therefore these distributions are used very extensively in mathematical statistics for interpretation of empirical data The paper continues ideas of the author’s works [15, 16] devoted to advanced based tools of
mathematical statistics The aim of the work is to generalize the well known theoretical and experimental results of statistical distributions of random values The Chi-square, Student and Fisher – Snedecor distributions are analyzed from the only point of view The application peculiarities are determined at the examination of the agree criteria of the empirical sample one with theoretical predictions of general population The numerical characteristics of these distributions are considered The theoretical and experimental results are generalized.
It is emphasized for the corrected amplification of the Chi-square, Student and Fisher – Snedecor distributions it is necessary to have the reliable empirical and testing data with the normal distribution. |
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URI:
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http://194.44.12.92:8080/jspui/handle/123456789/3421
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Date:
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2018 |