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目的:用贝塔函数研究牙弓曲线,探究牙弓曲线的主要决定因素。方法:用最小二乘法求解贝塔函数的曲度参数β,比较各牙齿的数据测量误差和数据缺失对β正确估算的影响。结果:男性上颌和下颌、女性上颌和下颌的β参数值分别为:0.708 2和0.723 6、0.701 0和0.714 5;用贝塔函数拟合牙弓曲线的拟合优度分别为:0.998 2和0.995 5、0.997 2和0.995 0。第一磨牙的数据测量误差和数据缺失对β正确估算影响较大。结论:第一磨牙和第二磨牙是男女上下颌牙弓曲线的主要决定因素。
OBJECTIVE: To study the curve of dental arch by beta function and to explore the main determinants of the curve of dental arch. Methods: The least square method was used to solve the curvature parameter β of the beta function, and the effect of data error and data loss on the correct estimation of β was compared. Results: The maxillary and mandibular values of the female were 0.708 2 and 0.723 6, 0.701 0 and 0.714 5 respectively for the upper and lower jaws. The goodness of fit of the dental arch curves fitted by the Beta function were 0.998 2 and 0.995 5, 0.997 2 and 0.995 0. The first molars data measurement error and data loss on the correct estimation of β greater impact. Conclusion: The first molars and the second molars are the main determinants of the arch curves of the maxillary and mandibular arch.