ABSTRACT

The logistic variable may assume negative values may discourage its use in reliability and other applications concerned with positive variables. For thick-tailed distributions it is sometimes helpful to trim off the smallest and largest order statistics due to their larger variance. Ratios of independent standard normal variables are distributed Cauchy. For normal signals in the absence of signals, the noise of the ratio would then be distributed Cauchy. The lognormal is related to the normal in the same way that the Weibull is related to the extreme-value distribution. Both the normal and lognormal have received considerable use in reliability and life-testing problems. The hazard function (HF) is a useful property to consider when selecting a model in life-testing problems since it can be interpreted in terms of wearout. Also densities or cumulative distribution functions which appear to have the same general shape may have considerably different HFs and thus can be distinguished on this basis.