泊松过程(一)

泊松分布描述的是给定的某段时间内,事件发生的概率

1.Poisson Process

1.1 Counting process

independent increment

注:增量是独立并且稳定的,同样服从泊松分布!!!!这个实际上是无记忆性!

Mean, Variance

下面通过例子理解:

如何构建泊松过程:

泊松过程描述的是给定的时间t之前发生的事件总数!!

1.2 Definition

泊松分布的定义,有以下两种

1.3 Properties

1.3.1 Decomposition

1.3.2 Superposition

举例应用:

1.4 Conditioanal distribution of arrival times

1.4.1


  • In other words, the time of the event should be uniformly distributed over [0, t]. 

1.4.2 Order statistics

  • Let Y1,Y2,...,Yn be n random variables. We say that Y(1),Y(2),...,Y(n) are the corresponding order statistics if Y(k) is the k th smallest

    value among Y1,Y2,...,Yn.

  • For instance,

    (Y1,Y2,Y3)=(4,5,1)
    The corresponding order statistics are

    (Y(1),Y(2),Y(3))=(1,4,5). 

下面是例子:

原文地址:https://www.cnblogs.com/Mr-ZeroW/p/7694850.html