MNO--PQRS
提出一种无需用户指定参数的算法，将非齐次泊松过程中的分段常数速率函数平滑为连续可微的分段二次函数，并保持期望到达数不变。
In both cyclic and finite-horizon contexts, piecewise-constant rate functions are commonly encountered in models with nonhomogeneous Poisson processes. We develop an algorithm, with no user-specified parameters, that returns a smoother rate function that maintains the expected number of arrivals. The algorithm proceeds in two steps: PQRS (Piecewise-Quadratic Rate Smoothing) returns a continuous and differentiable piecewise-quadratic function without regard to negativity. If negative rates occur, then MNO (Max Nonnegativity Ordering) returns the maximum of zero and another piecewise-quadratic function. MNO maintains continuity of rates and first derivatives, but with some exceptions. Our analysis allows fitting the MNO--PQRS function to require storage complexity of the order of the number of intervals and computational complexity of the order of the number of intervals squared. MNO--PQRS can be used as a stand-alone routine, or as an endgame for the authors’ earlier algorithm, I-SMOOTH.