METHOD FOR CONSTRUCTING A CONFIDENCE INTERVAL FOR THE VARIANCE OF A RANDOM VARIABLE
A.V. Ganicheva1, A.V. Ganichev2
1Tver State Agricultural Academy, Tver, Russian Federation
2Tver State Technical University, Tver, Russian Federation
Keywords: random variable, sample, variance, Chebyshev’s theorem, probability distribution law, number of observations
Abstract
The problem of reducing the number of observations for constructing a confidence interval of variance with a given degree of accuracy and reliability is considered. The new method of constructing an interval estimate of variance developed in the article is formulated by three statements and justified by four proven theorems. Formulas for calculating the required number of observations depending on the accuracy and reliability of the estimate are derived. The results of the calculations are presented in the table and shown in the diagram. The universality and effectiveness of this method is shown. The universality of the method lies in the fact that it is applicable to any laws of probability distribution, and not only for the normal law. The effectiveness of the developed method is justified by comparing its performance with other known methods.
|
