Abstract
In this paper, we first present explicit expressions for the maximum likelihood estimates (MLEs) of the location, and scale parameters of the Laplace distribution based on a Type-II right censored sample under different cases. Then, after giving the exact density functions of the MLEs, and the expectations, we derive the exact density of the MLE of the quantile, and utilize it to develop exact confidence intervals for the population quantile. We also briefly discuss the MLEs of reliability and cumulative hazard functions, and how to develop exact confidence intervals for these functions. These results can also be extended to any linear estimators. Finally, we present two examples to illustrate the inferential methods developed here.
| Original language | English |
|---|---|
| Article number | 7175066 |
| Pages (from-to) | 164-178 |
| Number of pages | 15 |
| Journal | IEEE Transactions on Reliability |
| Volume | 65 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 2016 |
| Externally published | Yes |
Keywords
- Best linear unbiased estimator
- Kaplan-Meier curve
- Laplace distribution
- P-P plot
- Q-Q plot
- confidence interval
- cumulative hazard function
- exact distribution function
- hypoexponential distribution
- maximum likelihood estimators
- mean square error
- quantile
- statistical bias
- type-II censoring
- variance