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:
 * $$\begin{align}

f(t)= & \frac{e^z}{\sigma {(1+{e^z})^{2}}} \\ z= & \frac{t-\mu }{\sigma } \\ \sigma > & 0 \end{align}$$
 * where:


 * $$ \mu = \text{location parameter,also denoted as }$$ $$\overline{T}$$


 * $$ \sigma=\text{scale parameter} $$

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