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A new distribution named intensive natural distribution is introduced withthe intent of consolidating statistics and empirical data. Based on theprobability derived from the Bernoulli distribution, this method extended alsoPoisson distribution to continuous, preserving its skewness. Using this model,the Horwitz curve has been explained. The theoretical derivation of our method,which applies to every kind of measurements collected through sampling, is heresupported by a mathematical demonstration and illustrated with severalapplications to real data collected from chemical and geotechnical fields. Wecompared the proposed intensive natural distribution to other widely usedfrequency functions to test the robustness of the proposed method in fittingthe histograms and the probability charts obtained from various intensivevariables.

Intensive natural distribution as Bernoulli success ratio extension to continuous: enhanced Gaussian, continuous Poisson, and phenomena explanation