A Python Code for Famispacing Estimation

Famispacing estimation, or family spacing estimation, is a quantitative method that estimates an individual's conformity or disconformity to an accepted minimum expectation (spacing interval scheme) within a population. It quantifies the similarity or dissimilarity between the observed pattern of biological children's ages and the expected pattern [2]. Within the framework of Kabirian-based optinalysis [1], famispacing is conceptualized as the isoreflective pairing between the observed and expected patterns of biological children's ages. The methodological processes in famispacing comprise two distinct phases: a) Preprocessing phase [2]: This involves applying preprocessing operations and transformations, such as parameter distillation, theoretical ordering, and shift transformations with absolutely no data centering. It also encompasses tasks like conceptual age pattern generation and optimizations within the established optinalytic construction. These optimizations include selecting an efficient pairing style, central normalization, and establishing an isoreflective pair between the two preprocessed data. The data are the observed and expected patterns of biological children's ages. b) Optinalytic model calculation phase [1]: This phase is focused on computing estimates (such as the Kabirian coefficient of conformity (similarity), the probability of conformity (similarity), and the disconformity (dissimilarity)) 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, Y.S. El-Sunais, H. Yusuf, M.S. Kaware, M. Suleiman, M.B. Isah, S.S. Yar’adua, S.S. Kankara, A. Bello, Famispacing: A Comprehensive and Sensitive Method for Family Spacing Estimation, (2024). Update the published citation details here. [You can follow the published version of the paper for the other reference details].生育间隔估计（famispacing estimation），又称家庭生育间隔估计，是一种量化方法，用于评估个体在群体中对公认的标准最小生育间隔方案的符合程度或偏离程度。该方法可量化亲生子女年龄的观测分布与预期分布之间的相似性与差异性[2]。 在基于卡比尔的最优分析（Kabirian-based optinalysis）框架[1]下，生育间隔估计被定义为亲生子女年龄的观测分布与预期分布之间的同反射配对（isoreflective pairing）。 生育间隔估计的方法学流程包含两个独立阶段： a) 预处理阶段[2]：该阶段需执行预处理操作与变换，例如参数蒸馏、理论排序以及完全不进行数据中心化的平移变换；同时还涵盖在既定最优分析框架下的概念化年龄分布生成与优化任务，其中优化内容包括选取高效配对模式、中心化归一化，以及在两组预处理后的数据间构建同反射配对。此处所用数据为亲生子女年龄的观测分布与预期分布。 b) 最优分析模型计算阶段[1]：该阶段基于卡比尔的同构最优分析模型，计算各类估计值，例如卡比尔符合度（相似性）系数、符合度（相似性）概率以及偏离度（差异性）。 参考文献： [1] K.B. Abdullahi. 基于卡比尔的最优分析：数学结构与生物序列中对称/非对称、相似/差异以及同一/非同一估计的概念化框架[J]. MethodsX, 2023, 11: 102400. https://doi.org/10.1016/j.mex.2023.102400 [2] K.B. Abdullahi, Y.S. El-Sunais, H. Yusuf, 等. 生育间隔估计：一种用于家庭生育间隔估计的全面且灵敏的方法[J]. 2024. 请在此处更新已发表的引用详情，可参考该论文的正式发表版本补充其余引用信息。