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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 unimodal. 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 Sshaped 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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 Spring '10
 Miskiad
 Normal Distribution, Variance, Probability theory, probability density function, logistic distribution

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