1P-Exponential MLE Solution with Right Censored Data

Compare the MLE solution and Fisher Matrix bound for a 1-parameter exponential distribution with right censored and complete failure data.

The formulas on page 166 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.


 * $$\hat{\theta}=\frac{TTT}{r}\ \ and\ \ se_{\hat{\theta}} = \frac{\hat{\theta}}{\sqrt{r}}\,\!$$

where TTT is the total test time and r is the number of failures.


 * $$\begin{align}

\hat{\theta} =& \frac{TTT}{r} = \frac{16+34+53+75+93+120+4\times 200}{6} = \frac{1191}{6} = 198.5 \\ \\ se_{\hat{\theta}} =& \frac{\theta}{\sqrt{r}} = \frac{198.5}{\sqrt{6}} = 81.037 \\ \end{align}\,\!$$

So the variance of $$ \hat{\theta}\,\! $$ is 6567.04