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, [math]\displaystyle{ cdf }[/math] and failure rate functions, it is sometimes preferred over the normal distribution, where these functions can only be obtained numerically. The [math]\displaystyle{ pdf }[/math] 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{ \mu = \text{location parameter,also denoted as } }[/math] [math]\displaystyle{ \overline{T} }[/math]

[math]\displaystyle{ \sigma=\text{scale parameter} }[/math]

The logistic distribution and its characteristics are presented in more detail in Chapter 10.