[This article belongs to Volume - 54, Issue - 04]
Gongcheng Kexue Yu Jishu/Advanced Engineering Science
Journal ID : AES-09-06-2022-203

Title : Analysis of Productive Functions Through Monotonic Transformation of Random Variables, Case of the Instantaneous Electrical Power Function
Alexander Borger, Juan M. Astorga,

Abstract : In this paper a methodology is introduced that allows probabilistic analysis of functions (transformations) generally associated with production, while preserving the parameters of the original transformation and having those a physical meaning. The resulting probability density function is customized to the phenomena that the transformation represents, phenomena from any discipline, such as management, economics, engineering, marketing, manufacturing, and other sciences. In the case of instantaneous electric power analysis, it is done through probabilities with first harmonic of current and voltage, and phase shift Φ. The time samples are re-sampled according to a uniform probability density function, so it is possible to apply transformation of random variables over this uniform density function. Depending on intrinsic values of the signal (the harmonic distortion, phase, amplitude), the shape of the instantaneous power signal (the transformation) varies and therefore the shape of the probability density function too. The model or methodology stablished here is general but limited to one independent variable used with a uniform sample function.