Authors R.B. Tregubov, M.V. Stremouhov
Month, Year 02, 2015 @en
Index UDC 621.391
Abstract Aim of this study is to find an approximation interval Clopper–Pearson provided out of the assumption that the frequency of occurrence of an event in n independent experiments (Bernoulli scheme) normal distribution. The practice shows that this assumption causes a serious error for the statistical analysis of rare events in a limited number of experiments. This object is achieved in the work by approximation the exact solution of the equations Clopper–Pearson with the help of sixth – degree polynomial. In turn, to obtain an accurate solution of the equations Clopper–Pearson used in the numerical method of bisection (method of bisection of the interval), implemented in an environment of mathematical modeling Mathcad. The value of the module of the proposed polynomial approximation (in a limited number n of independent experiments) error doesn’t exceed 5·10-3 . In turn, for the known approximation (in the same case) of the value of the module approximation error is much more, as evidence by the results of mathematical modeling Mathcad. The main results of the study are presented in tabular form coefficients of the approximating polynomials for different values of the confidence probability – β (0,9; 0,95; 0,99; 0,995 and 0,999) and number of tests – n (10; 20; 30… 100), the values of the polynominal to determine the left and right boundaries of the same parameter of the binominal distribution. A distinctive feature of the proposed method in the calculation of the boundaries of the confidence interval is that, firstly, the order of the approximating polynomial doesn’t depend on the namber of tests, and the coefficients of the boundary which is calculated; and secondly, eliminating the need to use the binomial distribution tables or approximating its beta distribution, F-distribution, normal distribution and Poisson distribution. The results can be applied for the analysis of probabilistic–temporal characteristics (loss probability PDUs transshipment, errors, not timely delivery etc.), communication systems for various purposes or their simulation models.

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Keywords Probability;relative frequency; point estimate; interval estimate; confidence interval; confidence probability; binomial distribution; Clopper–Pearson equation.
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