Template:LogisticDistribution: Difference between revisions
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===The Logistic Distribution=== | === The Logistic Distribution === | ||
The logistic distribution has a shape very similar to the normal distribution ( | |||
The < | 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> | ||
<br> | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
f(t)= & \frac{e^z}{\sigma {(1+{e^z})^{2}}} \\ | f(t)= & \frac{e^z}{\sigma {(1+{e^z})^{2}}} \\ | ||
| Line 8: | Line 8: | ||
\sigma > & 0 | \sigma > & 0 | ||
\end{align}</math> | \end{align}</math> | ||
The logistic distribution and its characteristics are presented in | <br>where: | ||
::<span class="texhtml">μ = location parameter,also denoted as </span><math>\overline{T}</math> | |||
::<span class="texhtml">σ = scale parameter</span> | |||
The logistic distribution and its characteristics are presented in detail in the chapter [[The Logistic Distribution]]. | |||
<br> | <br> | ||
Revision as of 16:16, 12 March 2012
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:
- [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:
- μ = location parameter,also denoted as [math]\displaystyle{ \overline{T} }[/math]
- σ = scale parameter
The logistic distribution and its characteristics are presented in detail in the chapter The Logistic Distribution.