Some Applications of Near-Order Statistics in Two-Parameter Exponential Distribution

Abstract

In this paper, some characterization results for exponential distribution are established. The results are concluded in terms of number of observations near of order statistics. It is shown that its probability mass function and its first moment can characterize the exponential distribution. Also, an estimator based on near-order statistics is introduced for tail thickness of exponential distribution.

Keywords

• Completeness properties
• Exponential distribution
• Müntz theorem
• Near-order statistics