Abstract:

One of the key procedures in statistical joint modeling is the determination of the joint size distribution. The mathematical features of the Poisson point process was considered. When the joint diameter distribution is continuous, the trace length lower bound must be zero; and the upper bound must be equal to the joint diameter upper bound. Since any continuous function could be fitted by a polynomial with high accuracy, a polynomial trace length distribution and constraints were proposed in the infinite sampling window for the Poisson disc joint model. Santalo closed-form integral solution was used to derive a closed-form expression for the equation, which determined the trace length distribution from the joint diameter distribution proposed by Warburton. Based on the polynomial trace length distribution, an analytical equation was derived to estimate the joint diameter distribution, and the complex numerical methods were avoided. The analytical equation was verified by the formula proposed by Priest. Based on the characteristic of the probability density function, a method for estimation of diameter distribution range was proposed, and the joint diameter lower bound was inferred by small step search algorithm. The inference method was checked for validity through Monte Carlo simulation.

Key words: joint network, Poisson disc joint model, joint diameter distribution, analytical method