|
|
| Line 1: |
Line 1: |
| === The Logistic Distribution ===
| | [[Category: For Deletion]] |
| | |
| 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, <span class="texhtml">''cdf''</span> and failure rate functions, it is sometimes preferred over the normal distribution, where these functions can only be obtained numerically. The <span class="texhtml">''pdf''</span> 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>\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 [[The Logistic Distribution]].
| |
| | |
| <br>
| |