泊松分布信息熵的性质和数值计算

The Character and Numerical Calculation for the Entropy of a Poisson Distribution

泊松分布的信息熵是参数λ的无穷级数.证明了泊松分布的信息熵是参数λ的单调递增凸函数;λ误差影响的条件数小于1;在保证精度的前提下,给出了信息熵的有限项求和的近似计算递推公式,解决了无穷级数求和及阶乘溢出的数值计算问题.

The entropy of a Poisson distribution was an infinite series about parameter λ.It was proved that the entropy of this distribution was a strictly increasing concave function about parameter λ,and its condition number was less than 1 about error influence of λ.For solving the problems of numerical calculation about summing an infinite series and overflow of factorial,a finite item summing recmrence formula of approximate calculation was given for the entropy of a Poisson distribution under the condition of ensuring accuracy.