矿床储量的最大熵分布模型研究

Model of the reserve-size distribution of ore deposits based on maximum entropy principle

根据最大熵原理,以熵作为矿床储量不确定性的量度,采用Lagrange乘子法给出矿床储量的概率密度函数解析式的统一表达式及实用的数值算法。当样本容量和单一矿体储量充分大时,得到储量的最佳密度函数是负指数函数;进一步对分布函数作适当修正,得到Weibull分布模型,并与Pareto定律进行比较,从分布的数学意义上分析这两种分布的内在联系,从而说明最大熵分布比Pareto律更能反映总体的分布规律。

Based on the maximum entropy principle and with entropy taken as the measurement of the uncertain ore reserves, a mathematical model of the deposits distribution is established. The optimal density function and general probability algorithm of the ore reserves are then derived by using the Lagrange multiplier method. When both the ore reserves and the sample capacity are sufficiently large, the density function is proved to decay exponentially as the deposits increase infinitely. The density function is further revised to a Weibull model. Comparing the Weibull distribution model with previously suggested ones such as Pareto distribution, it is concluded that the model based on the maximum entropy proposed in the paper presents a more faithful picture of the general distribution of the ore deposits.