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| === The Logistic Distribution ===
| | #REDIRECT [[The Logistic Distribution]] |
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| 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>
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| ::<math>\begin{align}
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| f(t)= & \frac{e^z}{\sigma {(1+{e^z})^{2}}} \\
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| z= & \frac{t-\mu }{\sigma } \\
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| \sigma > & 0
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| \end{align}</math>
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| <br>where:
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| ::<span class="texhtml">μ = location parameter,also denoted as </span><math>\overline{T}</math>
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| ::<span class="texhtml">σ = scale parameter</span>
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| The logistic distribution and its characteristics are presented in detail in the chapter [[The Logistic Distribution]].
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| <br>
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