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Engineering Statistics Handbook Episode 1 Part 6

Tham khảo tài liệu 'engineering statistics handbook episode 1 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1.3.3.14.5. Histogram Interpretation Bimodal Mixture of 2 Normals hW ENGINEERING STATISTICS HANDBOOK TOOLS raids ISEAtCH back NEKT 1. Exploratory Data Analysis 1.3. EDA Techniques 1.3.3. Graphical Techniques Alphabetic 1.3.3.14. Histogram 1.3.3.14.5. Histogram Interpretation Bimodal Mixture of 2 Normals Histogram from Mixture of 2 Normal Distributions Discussion of Unimodal and Bimodal The histogram shown above illustrates data from a bimodal 2 peak distribution. In contrast to the previous example this example illustrates bimodality due not to an underlying deterministic model but bimodality due to a mixture of probability models. In this case each of the modes appears to have a rough bell-shaped component. One could easily imagine the above histogram being generated by a process consisting of two normal distributions with the same standard deviation but with two different locations one centered at approximately 9.17 and the other centered at approximately 9.26 . If this is the case then the research challenge is to determine physically why there are two similar but separate sub-processes. http www.itl.nist.gov div898 handbook eda section3 eda33e5.htm 1 of 2 5 1 2006 9 56 39 AM 1.3.3.14.5. Histogram Interpretation Bimodal Mixture of 2 Normals Recommended Next Steps If the histogram indicates that the data might be appropriately fit with a mixture of two nonnal distributions the recommended next step is Fit the normal mixture model using either least squares or maximum likelihood. The general normal mixing model is M pộl 1 -p 02 where p is the mixing proportion between 0 and 1 and 01 and are nonnal probability density functions with location and scale parameters 1 fli P2 and 2 respectively. That is there are 5 parameters to estimate in the fit. Whether maximum likelihood or least squares is used the quality of the fit is sensitive to good starting values. For the mixture of two nonnals the histogram can be used to provide initial estimates for the location and .