A Python Code for Statistical Mirroring
Description
Statistical mirroring is the measure of the proximity or deviation of transformed data points from a specified location estimate within a given distribution [2]. Within the framework of Kabirian-based optinalysis [1], statistical mirroring is conceptualized as the isoreflectivity of the transformed data points to a defined statistical mirror. This statistical mirror is an amplified location estimate of the distribution, achieved through a specified size or length. The location estimate may include parameters such as the mean, median, mode, maximum, minimum, or reference value [2]. The process of statistical mirroring comprises two distinct phases: a) Preprocessing phase [2]: This involves applying preprocessing transformations, such as compulsory theoretical ordering, with or without centering the data. It also encompasses tasks like statistical mirror design and optimizations within the established optinalytic construction. These optimizations include selecting an efficient pairing style, central normalization, and establishing an isoreflective pair between the preprocessed data and its designed statistical mirror. b) Optinalytic model calculation phase [1]: This phase is focused on computing estimates based on Kabirian-based isomorphic optinalysis models. References: [1] K.B. Abdullahi, Kabirian-based optinalysis: A conceptually grounded framework for symmetry/asymmetry, similarity/dissimilarity, and identity/unidentity estimations in mathematical structures and biological sequences, MethodsX 11 (2023) 102400. https://doi.org/10.1016/j.mex.2023.102400 [2] K.B. Abdullahi, Statistical mirroring: A robust method for statistical dispersion estimation, MethodsX 12 (2024) 102682. https://doi.org/10.1016/j.mex.2024.102682