Logistic law

In Probability, the logistic law of parameter μ and S > 0 is a Loi of probability whose density is

$f\; (X)\; =\; \backslash \; frac\; \{e^\; \{-\; \backslash \; frac\; \{X\; \backslash \; driven\}\; \{S\}\}\}\; \{S\; \backslash \; left\; (1+e^\; \{-\; \backslash \; frac\; \{X\; \backslash \; driven\}\; \{S\}\}\; \backslash \; right)\; ^2\}$

Its function of distribution is

$F\; (X)\; =\; \backslash \; frac\; \{1\}\; \{1+e^\; \{-\; \backslash \; frac\; \{X\; \backslash \; driven\}\; \{S\}\}\}$

Its name of logistic law is resulting owing to the fact that its density of probability is a logistic function Its hope and its variance are given by the following formulas:

$E\; (X)\; =\; \backslash \; driven\; \backslash ,$

$V\; (X)\; =\; \backslash \; frac\; \{s^2\; \backslash \; pi^2\}\; \{3\}$

It is used in logistic Régression

The logistic law standard is the logistic law of parameter 0 and 1.

Its Fonction of distribution is the sigmoid

$F\; (X)\; =\; \backslash \; frac\; \{1\}\; \{1+e^\; \{-\; X\}\}$

Its hope and its variance are given by the following formulas:

$E\; (X)\; =\; 0\; \backslash ,$

$V\; (X)\; =\; \backslash \; frac\; \{\backslash \; pi^2\}\; \{3\}$

See too

• logistic function
• logistic Regression
• Logit

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