5、概率循环分布的有效估计

概率循环分布的有效估计

在概率编程中，准确估计随机变量的分布是一项关键任务。本文将介绍一种基于最大熵（ME）和Gram - Charlier展开（GC）的算法，用于估计概率循环中随机变量的分布，并通过统计测试评估估计的准确性。

算法概述

下面是有效分布估计的算法：

Algorithm 1. Effective Distribution Estimation
Input: Probabilistic loop P with program variable(s) x;
set M of exact moments of x for loop iteration n of P
Output: Estimated distributions fME and fGC of x, with respective accuracy
AME and AGC
Parameters: Loop iteration n ∈N; number of executions e ∈N of P
Initialization:
1: Choose a subset of exact moments SM = {E(x), E(x2),..., E(x|SM|)} ⊂M
2: Collect SampleData by sampling e many P variable values at the nth loop
iteration
Distribution Estimation:
3: Compute fME using SM and ME as in (5)
4: Compute fGC using SM and GC as in (