Date of Award
Master of Science (MS)
Mathematics and Statistics
Rex L. Hurst
In statistical experiments, if a random sample of items drawn from a population is tested until all items fail, conventional statistical techniques may be employed but normal frequency distributions may not be satisfied. Failure of the data to satisfy the assumption of normality may lead to an invalid result. Some statistical results, however, have been shown to be robust to the failure of the data to meet normality. When using conventional experimental methods, considerable time and money are required to produce failure of all samples. To be economical, many experiments are concluded before all test items fail. A sample obtained from such experiments is said to be truncated or censored.
By truncation, or censoring, the information can be obtained in a shorter period of time, since fewer items are tested. These statistical situations have frequently been encountered in what are called life testing, dosage response studies, target analysis, biological analysis, biological assays, and in other related investigations.
The methods applicable to the study of truncation may be classified roughly as follows: 1. Method of maximum likelihood estimator. This method is to be recommended when sample sizes are at least moderately large.The estimators for truncated and censored samples are consistent and asymptotically efficient. Solutions are always approximated by straightforward iterative procedures; hence, the calculations often become tedious and laborious. 2. Method of least squares or order statistics. The method should be employed when estimators must be based on samples of size 20 or less. The approach to the general case in truncation is of value not only for its numerical results but also for the drawing of inferences concerning interesting and important patterns for the coefficients, variances, and the relative efficiencies of the estimates. 3. Computer method of maximum likelihood estimation. Recently with the development and availability of electronic computers, the exhausting calculations involved in the maximum likelihood estimations have been greatly alleviated. One program furnished by Hurst (1966) has been appended for reference.
Liang, Kuo-chung, "Estimation of Parameters of Normal Populations from Truncated Samples" (1967). All Graduate Plan B and other Reports. 1115.
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