S形分布的数据拟合数学模型研究

基金项目: 国家自然科学基金资助项目(40671154,40701158)

详细信息

Study of Mathematic Model for Fitting S Shape Distributed Data

¹School of Resource and Environment Science,Wuhan University,129 Luoyu Road,Wuhan 430079,China

Funds: 国家自然科学基金资助项目(40671154,40701158)

摘要: S形曲线有着广泛的应用,以往的研究模型仅含三个参数,大多以对称S形分布的基本光滑数据为例,这使得自由度受限的和以理想数据为研究对象所得到的研究结果难以适用于更实际的、非对称(左偏S形分布、右偏S形分布)的非光滑观测数据。为此,提出并建立了含有5个参数的二次有理模型,作为对S形分布的观测数据进行拟合的模型,并进一步分为带导数拟合、5分段和值拟合和5特征点拟合,使S形分布的各种情况(左偏、对称和右偏)的拟合得到明显改善。
- S形分布 /
- 数据似合 /
- Logistic模型 /
- Gompertz模型 /
- 有理模型
Abstract: S shape curve(sigmoid) has an application in many fields.Most of the previous models contain only 3 parameters and take the symmetric and smooth S shape curve as fitting object so that it these fitting models can not be adapted to other more real situations: asymmetric and zigzag S shape distributed data.Therefore,author has created a "2 order rational data fitting model" which contains 5 parameters so that obtains more freedom for fitting the S shape distributed data.The Fitting experiments have clearly expressed that the suggested method obtains more advantages and can well fit different S shape curves considerably.
- S shape distribution /
- data fitting /
- Logistic model /
- Gompertz model /
- rational model