Проверка гипотезы о виде распределения по интервальным данным
| Jazyk: | ruština |
|---|---|
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Вестник Томского государственного университета. Управление, вычислительная техника и информатика. |
| ISSN: | 2311-2085 1998-8605 |
| Popis: | Рассматривается ICM(Iterative Convex Мтогап^-алгоритм построения непараметрической оценки функции распределения по интервальным данным. Предлагаются критерии согласия, основанные на расстоянии между предполагаемой функцией распределения и её непараметрической оценкой. Применение критериев согласия опирается на статистическое моделирование условных распределений статистик данных критериев в интерактивном режиме проверки гипотезы о виде распределения. The main terms of interval data analysis was initially founded the measurement theory in metrology where an interval uncertainty is naturally introduced. It is expected that every observation is measured by an instrument with absolute error Д. Thus, if the precise value of an observed response is x, measurement error is e e [-Д, Д], then the measurement is equal to x = x + e. In this case, we deal with a usual complete sample Xn = {Xj,...,Xn}. Nevertheless, the measurement can be represented as an interval (x -Д, x + Д) = (L, R). In this case, for the sample of n observations we obtain an interval sample of the form In ={( A, R1),..., (Ln, Rn)}. The main idea of nonparametric estimation of the distribution function with interval data is based on maximization of the loglikelihood function ln L (In )=£ ln (F (R) F (Lt)) i =1 at the boundary points of observations Li, Ri, i = 1, n, under condition of monotonicity of the distribution function. The Turnbull and ICM algorithms are used for calculation of the nonparametric estimate of the distribution function with interval data. The accuracy of the estimates calculation is the same for both algorithm, but the computing time is less for the ICM algorithm. Unknown distribution parameters can be estimated by the maximum likelihood method, which is based on the maximization of likelihood function by parameter 8 : L (Inl8) = n (F(Ri | 8) F(Li | 8)). i=1 Thus, the maximum likelihood estimates can be written as 8 = arg max ln L (In | 8). 8e© In this paper, the modifications of the classical goodness-of-fit tests for composite hypothesis H0 : F(t) e {F0(t; 8), 8 e ©} have been proposed. The main idea of this modification is based on the usage of nonparametric estimate of the distribution function, obtained by the ICM algorithm, instead of the empirical distribution function. In this case, we have the test statistic of the Kolmogorov type as Dn = sup \Fn(t)-F0(t,8), 0-f0 8 where Fn(t) is the nonparametric estimate of the distribution function by the interval data, 0 < x0 < x1 |
| Databáze: | OpenAIRE |
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