Pitman Closeness of Maximum Likelihood Estimators Under Type-II Hybrid Censoring With Exponential Lifetime
| dc.contributor.advisor | Davies, Katherine | |
| dc.contributor.author | Ly, Anna | |
| dc.contributor.department | Statistics | en_US |
| dc.date.accessioned | 2025-10-29T15:43:41Z | |
| dc.date.available | 2025-10-29T15:43:41Z | |
| dc.date.issued | 2025-11 | |
| dc.description.abstract | The Pitman closeness (PC) criterion is a method to compare two statistical estimators. Assuming that the lifetime data follow an exponential distribution with scale parameter $\theta$, prior work had computed the PC probabilities for estimators of $\theta$ based on Type-I right-censoring, Type-II right-censoring and Type-I hybrid censoring schemes (HCS). However, the derivation of the PC under a Type-II HCS has not yet been addressed in the literature. This thesis examines two comparisons of maximum likelihood estimators for $\theta$, the scale parameter, for exponentially distributed lifetimes arising from the Type-II HCS: (1) between estimators corresponding to different numbers of observed failures, and (2) between estimators with different censoring times. Closed-form expressions for the PC probabilities are derived, and numerical results are reported for various sample sizes, censoring times, and study durations. Numerical results show that increasing the pre-fixed termination time or the number of failures led to an estimator that was always Pitman closer to the true parameter. These findings confirm the intuition that increasing the termination time or the number of observed failures will usually lead to an estimator that is Pitman closer than one based on a shorter termination time or fewer observed failures. | en_US |
| dc.description.degree | Master of Science (MSc) | en_US |
| dc.description.degreetype | Thesis | en_US |
| dc.description.layabstract | Researchers are often interested in the time it takes for a certain event to happen. For example, in medical studies, we may ask how long it takes a patient to recover, while in engineering, we may study how long a product works before it fails. This type of information, which measures the time until an event occurs, is called lifetime data. Collecting such data can be difficult because studies often end before every recovery or failure has been observed, resulting in incomplete data. To make sense of incomplete data, statisticians use statistical inference, a process where they make inferences about the population from available data. There is a special type of statistical inference, called estimation, where mathematical formulas called estimators are used to approximate important features of said population. This thesis examines how to decide which estimator is more accurate among a given class under a specific data collection scheme. Using a mathematical tool called the Pitman closeness criterion, we derive and compute exact expressions for making pairwise comparisons among three different estimators that depend on the length of the study and the number of observations collected. Our results, based on this criterion, support the intuitive idea that extending the study period or increasing the number of observations leads to producing a better estimator according to the Pitman closeness criterion in a particular data collection scheme. | en_US |
| dc.identifier.uri | http://hdl.handle.net/11375/32609 | |
| dc.language.iso | en | en_US |
| dc.subject | Pitman Closeness | en_US |
| dc.subject | Maximum Likelihood Estimators | en_US |
| dc.subject | Hybrid Censoring | en_US |
| dc.subject | Exponential Distribution | en_US |
| dc.title | Pitman Closeness of Maximum Likelihood Estimators Under Type-II Hybrid Censoring With Exponential Lifetime | en_US |
| dc.type | Thesis | en_US |