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Abstract
The paper provides a series representation of the logistic probability density function in terms of differently scaled double exponential distributions with terms of the series alternating in signs. This representation is used to calculate moments, moment generating function, and characteristic function of a logistic distribution. The same representation is also used to derive the logistic distribution as the scale mixture of a normal distribution. © 2010 Springer Science+Business Media, LLC.
Keywords
Double exponential, Generating functions, Moments, Normal, Scale mixture, Series representation
Source Title
tThe Legacy of Alladi Ramakrishnan in the Mathematical Sciences
Publisher
Series/Report No.
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Date
2010
DOI
10.1007/978-1-4419-6263-8_21
Type
Others