An heuristic approximation of the sampling distribution of the coefficient of variation
Résumé
The applicability of the stress-strength method to mechanical dimensioning necessitates some knowledge about the statistical distribution of two characteristics. Product fiability results from their sensitivity to variability, measured in practice by the coefficient of variation. The sampling distribution of its estimator is quite cumbersome. Thus, in the normal case, one should use the non-central Student distribution. We present a simple analytical approximation, which tries to avoid such complexities in the small sample context. Our proposal is based on the derivation of Gaussian quantiles, and seems accurate enough for practical purposes in the range of values generally met in practice