Template:LogisticDistribution

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, cdf and failure rate functions, it is sometimes preferred over the normal distribution, where these functions can only be obtained numerically. The pdf of the logistic distribution is given by:

[math]\displaystyle{ \begin{align} f(t)= & \frac{e^z}{\sigma {(1+{e^z})^{2}}} \\ z= & \frac{t-\mu }{\sigma } \\ \sigma \gt & 0 \end{align} }[/math]

where:

[math]\displaystyle{ \begin{align} \mu = & \text{location parameter (also denoted as }\overline{T}) \\ \sigma = & \text{scale parameter} \end{align} }[/math]

The logistic distribution and its characteristics are presented in detail in The Logistic Distribution.