Logistic-01 - Logistic Distribution Raminta Stockute Andrea...

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Unformatted text preview: Logistic Distribution Raminta Stockute, Andrea Veaux, Paul Johnson May 1, 2006 1 Introduction The Logistic distribution is a continuous probability density function that is symmetric and uni-modal. It is similar in appearance to the Normal distribution and in practical ap- plications, the two distributions cannot be distinguished from one another. 2 Mathematical Definition This distribution is characterized by two main parameters: location μ and scale σ . The probability density function is: f ( x ) = e- ( x- μ ) /σ σ (1 + e- ( x- μ ) /σ ) 2 . The cumulative distribution of the Logistic a familiar S-shaped curve which will be fa- miliar to studennts of Logistic regression: F ( x ) = 1 1 + e- ( x- μ ) /σ . 3 Moments The expected value is equal to the location parameter, μ : E ( x ) = μ Because the distribution is symmetric, the median and the mode are also equal to μ . The variance of this distribution is: V ar ( x ) = 1 3 ( πσ ) 2 ....
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Logistic-01 - Logistic Distribution Raminta Stockute Andrea...

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