Doctoral Dissertations


"In this work, a saddlepoint-based method is developed for generating small sample confidence bands for the population survival function from the Kaplan-Meier (KM), the product limit (PL), and Abdushukurov-Cheng-Lin (ACL) survival function estimators, under the proportional hazards model. In the process the exact distribution of these estimators is derived and developed mid-population tolerance bands for said estimators. The proposed saddlepoint method depends upon the Mellin transform of the zero-truncated survival estimator which is derived for the KM, PL, and ACL estimators. These transforms are inverted via saddlepoint approximations to yield highly accurate approximations to the cumulative distribution functions of the respective cumulative hazard function estimators and these distribution functions are then inverted to produce saddlepoint confidence bands. The saddlepoint confidence bands for the KM, PL and ACL estimators is compared with those obtained from competing large sample methods as well as those obtained from the exact distribution. In the simulation studies it is found that the saddlepoint confidence bands are very close to the confidence bands derived from the exact distribution, while being much easier to compute, and outperform the competing large sample methods in terms of coverage probability"--Abstract, page iii.


Paige, Robert

Committee Member(s)

Samranayake, V. A.
Wen, Xuerong Meggie
Olbricht, Gayla R.
Du, Xiaoping


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics


Missouri University of Science and Technology

Publication Date

Spring 2016


x, 77 pages

Note about bibliography

Includes bibliographic references (pages 74-76).


© 2016 Emad Mohamed Abdurasul, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11355

Electronic OCLC #


Included in

Mathematics Commons