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Dissertation
Practical applications and properties of the Exponentially Modified Gaussian (EMG) distribution
Doctor of Philosophy (Ph.D.), Drexel University
23 Mar 2011
DOI:
https://doi.org/10.17918/etd-3463
Abstract
The exponentially modified Gaussian (EMG) probability distribution is defined as the convolution of an exponential distribution and a Gaussian distribution which are independent of each other. Using a reparameterized form of the EMG cumulative distribution function (cdf) several properties of the EMG distribution are derived. These properties are used to test whether the distribution of the perfect match (PM) probes from five Affymetrix microarrays follows an EMG distribution and to create a new parameter estimation method. A commonly used method for preprocessing Affymetrix microarray data, known as the robust multi-array average (RMA), assumes that the distribution of the PM probes at least approximately follows an EMG distribution. Using the results derived in this thesis it is found that the EMG distribution is not a good t for these sample data based on differences in the right tail of the sample distribution. A new distribution that is very dissimilar to the right tail of an EMG distribution is derived that more accurately fits the right tail of the sample data. From the properties of the EMG distribution derived in this thesis it is further shown that a new parameter estimation method can be created. This new parameter estimation method is compared against two other methods from the literature namely the method of moments and the Silver method (2009). From a theoretical perspective, the new parameter estimation method has the advantage that it is proven to be consistent and to always return valid parameter estimates (such as the constraint that the variance be positive). Neither the Silver method nor the method of moments has both of these qualities. All three methods were compared on the same syntheticdata generated from EMG distributions and it was found that the performance of each method depended on the "shape of the EMG distribution. It was also found that the Silver method appears to not be consistent for EMG distributions that are too "close to being a Gaussian distribution.
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Details
- Title
- Practical applications and properties of the Exponentially Modified Gaussian (EMG) distribution
- Creators
- Scott Haney - DU
- Contributors
- Moshe Kam (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Engineering (1970-2026); Electrical (and Computer) Engineering [Historical]; Drexel University
- Other Identifier
- 3463; 991014632180004721