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| ===The Logistic Distribution===
| | #REDIRECT [[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>cdf</math> and failure rate functions, it is sometimes preferred over the normal distribution, where these functions can only be obtained numerically.
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| The <math>pdf</math> of the logistic distribution is given by:
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| <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>
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| where:
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| ::<math> \mu = \text{location parameter,also denoted as }</math> <math>\overline{T}</math>
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| ::<math> \sigma=\text{scale parameter} </math>
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| The logistic distribution and its characteristics are presented in more detail in Chapter [[The Logistic Distribution]].
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| <br>
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