Reconstruction of Probability Density Function for Gamma Distribution

• 作者: FAN Jinwei LI Zhongsheng TIAN Bin
• 来源期刊: 东华大学学报（英文版）
• 学科: 数学
• 年，卷（期）: 2020,（4）
• 页码范围: 327-333
• 页数: 7页
• 分类号: O213.2
• 语种: 英文

摘要

The probability distributions of small sample data are difficult to determine, while a large proportion of samples occur in the early failure period, so it is particularly important to make full use of these data in the statistical analysis. Based on gamma distribution, four methods of probability density function ( PDF ) reconstruction with early failure data are proposed, and then the mean time between failures ( MTBF ) evaluation expressions are concluded from the reconstructed PDFs. Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data. The reconstruction methods of PDF also have certain guiding significance for other distribution types.