Abstract:An ordered set of probability sensity functions was derived form transforms of the normal distribution. Variate transforms are based on orders of exponentiation. The set of distributions includes the log‐normal. a partial basis for use of these functins in hydrology is demonstrated by establishing some required properties. A concept of mixed samples of zero and nonzero elements forming nonseparable sets of virtual and real elements is introduced to establish a physical lower limit of sampled diata independent of functional bound