Abstract
Until this chapter, we have looked almost exclusively at CUSUM schemes for the normal distribution. We now take a detailed look at two other continuous members of the exponential family of distributions (the gamma and the inverse Gaussian) and their CUSUMs. We find that the design of CUSUMs for these distributions differs from the normal distribution; in particular, and sometimes the optimal CUSUM involves CUSUMming a transformed variable.
Many years ago I called the Laplace-Gaussian curve the NORMAL curve, which name, while it avoids an international question of priority, has the disadvantage of leading people to believe that all other distributions of frequency are in one sense or another “abnormal.”. That belief is, of course, not justifiable. Karl Pearson
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© 1998 Springer Science+Business Media New York
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Hawkins, D.M., Olwell, D.H. (1998). Other continuous distributions. In: Cumulative Sum Charts and Charting for Quality Improvement. Statistics for Engineering and Physical Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1686-5_4
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DOI: https://doi.org/10.1007/978-1-4612-1686-5_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7245-8
Online ISBN: 978-1-4612-1686-5
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