Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




N. Balakrishnan


In this thesis we generalize several recurrence relations for moments of order statistics from I.I.D. random variables to I.NI.D. random variables. By considering the multiple outlier model as a special case, these I.NI.D. recurrence relations will enable use to compute all of the means, variances, and covariances of all order statistics from a sample (possibly) containing multiple outlier in a simple recursive manner. We will then use these results to address the problem of robust estimation of parameters in the presence of multiple outliers by examining the bias and mean square error of various linear estimators of the parameters of the underlying population. We will initiate work on the multiple outlier model for the logistic and Pareto distributions by deriving I.NI.D. recurrence relations, the Laplace distribution by making use of the results of Balakrishnan (1994a) who derived recurrence relations for the I.NI.D. exponential model, and the exponential model by providing an alternative method of proof for the results of Balakrishnan (1994a) and generalizing them to the I.NI.D. doubly truncated exponential model. In addition, we will consider tests for outliers. We will initiate work on testing for outliers when the underlying populations have the Laplace and logistic distributions and then examine and compare the performance of various test statistics based on certain power criteria. We also derive maximum likelihood estimators, conditional confidence intervals, and conditional tolerance intervals for the Laplace distribution based on Type-II right censored-samples and also some extensions to generally censored samples.

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Mathematics Commons