SIU-Based Modification in Kelley’s Measure of Skewness to Achieve Gains in Efficiency

摘要

The importance of accurate modeling of life-lengths of components and systems cannot be over-emphasized. Some well-known distributions such as the Birnbaum Saunders distribution extensively used in Reliability Theory are known to fulfill the self-inversion property, the term ‘Self-Inverse at Unity’ (‘SIU’) implying that, for a random variable X , the distribution of 1/ X is identical to the distribution of X . Very recently, it has been demonstrated the advantage that can be drawn from the SIU property by proposing a modification to the well-known formula of the empirical cumulative distribution function to obtain an estimator of the cumulative distribution function that is more efficient than the empirical cumulative distribution function in situations where the parent population can be assumed to be SIU. Subsequently, a number of papers have appeared proposing SIU-based modifications to the formulae of well-known estimators of central tendency, dispersion and kurtosis that are likely to yield gains in efficiency on account of an approach very similar to the one adopted for the modification of the formula of the empirical cumulative distribution function. In this paper, we propose SIU-based modification to Kelley’s Measure of Skewness and, through a simulation study, demonstrate the potential of the proposed formula in improving the efficiency of the estimation process which, obviously, has important implications for accurate modeling of life-data encountered in various branches of engineering.