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===The Logistic Distribution===
#REDIRECT [[The Logistic Distribution]]
The logistic distribution has a shape very similar to the normal distribution (''i.e.'' bell shaped), but with heavier tails. Since the logistic distribution has closed form solutions for the reliability, <math>cdf</math> and failure rate functions, it is sometimes preferred over the normal distribution, where these functions can only be obtained numerically.
The <math>pdf</math> of the logistic distribution is given by:
<br>
::<math>\begin{align}
  f(t)= & \frac{e^z}{\sigma {(1+{e^z})^{2}}} \\
  z= & \frac{t-\mu }{\sigma } \\
\sigma > & 0 
\end{align}</math>
<br>
where:
::<math> \mu = \text{location parameter,also denoted as }</math> <math>\overline{t}</math>
::<math> \sigma=\text{scale parameter} </math>
<br>
The logistic distribution and its characteristics are presented in more detail in [[The Logistic Distribution|Chapter 14]].
 
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Latest revision as of 09:57, 9 August 2012