Editing Exponential distribution (section)

===Confidence intervals===
An exact 100(1 − α)% confidence interval for the rate parameter of an exponential distribution is given by:<ref>{{cite book| title=Introduction to probability and statistics for engineers and scientists|first=Sheldon M.|last=Ross| page=267| url=https://books.google.com/books?id=mXP_UEiUo9wC&pg=PA267| edition=4th|year=2009| publisher=Associated Press| isbn=978-0-12-370483-2}}</ref>
<math display="block">\frac{2n}{\widehat{\lambda}_{\textrm{mle}} \chi^2_{\frac{\alpha}{2},2n} }< \frac{1}{\lambda} < \frac{2n}{\widehat{\lambda}_{\textrm{mle}}  \chi^2_{1-\frac{\alpha}{2},2n}}\,,</math>
which is also equal to
<math display="block">\frac{2n\overline{x}}{\chi^2_{\frac{\alpha}{2},2n}} < \frac{1}{\lambda} < \frac{2n\overline{x}}{\chi^2_{1-\frac{\alpha}{2},2n}}\,,</math>
where {{math|χ{{su|p=2|b=''p'',''v''}}}} is the {{math|100(''p'')}} [[percentile]] of the  [[chi squared distribution]] with ''v'' [[degrees of freedom (statistics)|degrees of freedom]], n is the number of observations and x-bar is the sample average. A simple approximation to the exact interval endpoints can be derived using a normal approximation to the {{math|''χ''{{su|p=2|b=''p'',''v''}}}} distribution. This approximation gives the following values for a 95% confidence interval:
<math display="block">\begin{align}
  \lambda_\text{lower} &= \widehat{\lambda}\left(1 - \frac{1.96}{\sqrt{n}}\right) \\
  \lambda_\text{upper} &= \widehat{\lambda}\left(1 + \frac{1.96}{\sqrt{n}}\right)
\end{align}</math>

This approximation may be acceptable for samples containing at least 15 to 20 elements.<ref name="Guerriero-2012">{{Cite journal | first1 = V. | last1= Guerriero | year = 2012  | title = Power Law Distribution: Method of Multi-scale Inferential Statistics| journal = Journal of Modern Mathematics Frontier | url =https://www.academia.edu/27459041 | volume = 1  | pages = 21–28}}</ref>