Best unbiased prediction of order statistics in stable distributions

ABSTRACT

We introduce the best unbiased prediction of missing order statistics of a stable distribution, based on conditional expected value. We present necessary and sufficient conditions for the existence of conditional moments of stable order statistics. These conditions enable us to compute unknown parameters using the expectation-maximization algorithm. We reveal the efficiency of the presented method through a simulation study.

KEYWORDS:

• EM algorithm
• Order statistics
• Prediction
• Stable distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G30
• 60E07

Acknowledgment

The authors would like to thank anonymous reviewers for their corrections, comments, and suggestions to improve the manuscript.