Construction of an Integral Distribution Function of Random Variables Determining the Impact of Wind Power Plant on Birds in accordance with the Predictive Analysis by Experts

Abstract

The team of scientists led by ornithologist V. D. Siokhin proposed a method for predicting the impact of planned wind power plants (WPP) on avifauna using expert assessment. The method for modeling the differential p(x) and integral F(x) distribution functions of the sum of several random variables with distribution densities p1(x1), p2(x2), p3(x3)…, determining the probability of bird interaction on the territory of a wind farm and adjacent buffer zones is developed in this article. The function p(x), which is a convolution of p1(x1), p2(x2), p3(x3) ..., is represented as an improper integral with infinite limits. An algorithm for calculating p(x) and F(x) is proposed by replacing an improper integral with an integral having finite limits and subsequent numerical integration taking into account the specified accuracy. Testing of the method for calculating the functions p(x) and F(x) was carried out on two examples with known solutions. One of the tests was carried out on two differential functions of distribution subjecting the normal law with mathematical expectations а1 and а2, and variances σ1 2 and σ2 2 . It is known that the distribution of such a sum obeys the normal law with mathematical expectation a equal to the sum of а1 and а2, and variance σ 2 equal to the sum of σ1 2 and σ2 2 . The results of calculations of the functions p(x) and F(x) using numerical methods for the number of nodes of 100 and more coincide with known solutions with an error of 10-15, which indicates the high accuracy of the proposed method. The found integral distribution function allows us to determine the probability characteristics of the impact of wind farms on birds.

Keywords

• Integration
• Mathematical statistics
• Numerical method
• Random variable distribution function.

References

1. Yeremeev, V., Naidysh, A., & Strokan, O. (2024). Constructıon of an integral distribution function of random variables determining the impact of wind power plant on birds in accordance with the predictive analysis by experts. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 30, 9-16.