RESEARCH PAPER
Research on Parameters Estimation Method of Three-Parameters Log-Normal Distribution for Automotive Batteries under Small Sample Data
1
School of Mechanical and Aerospace Engineering, Jilin University, China
2
Key Laboratory of CNC Equipment Reliability, Ministry of Education, China
3
NEV Inst, China FAW Group Co., Ltd., China
Submission date: 2026-01-15
Final revision date: 2026-03-01
Acceptance date: 2026-03-23
Online publication date: 2026-04-02
Corresponding author
KEYWORDS
Parameter estimationSmall sample sizeAutomotive batteriesThree-parameter log-normal distributionCumulative sum of squared errors
TOPICS
ABSTRACT
To address the issue that the classical LSE and MLE neglect global errors when estimating the two parameters of the log-normal distribution with small samples, a three-parameter estimation method integrating empirical distribution function model optimization, threshold parameter estimation, and cumulative sum of squared errors minimization is proposed. The initial dataset is derived via inverse transformation of the empirical distribution, and the empirical distribution model is optimized using the linear correlation coefficient. The interpolation method is employed to estimate the threshold parameter corresponding to the maximum linear correlation coefficient. The particle swarm optimization （PSO） algorithm optimizes the location and scale parameters to minimize the cumulative sum of squared errors. The K-S test is applied to evaluate the fitting performance, and the RMSE is used as an indicator to verify the accuracy of the proposed method. An empirical study is conducted by combining 13 sets of actual lifetime data and simulated data of a certain automotive battery.
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| eISSN: | 2956-3860 |
| ISSN: | 1507-2711 |
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