如何用英语简单解释泊松分布和指数
泊松分布与指数分布
Poisson distribution and exponential distribution
假设一事件在任何长为t的时间内出现故障的次数v(t)服从参数为it的泊松分布,则相邻两次事件的时间间隔T服从参数为i的指数分布。
Suppose that a failure in any event for t long time v (T) to the number of parameters for the distribution of it Poisson, is adjacent to the two event time interval T obey...全部
泊松分布与指数分布
Poisson distribution and exponential distribution
假设一事件在任何长为t的时间内出现故障的次数v(t)服从参数为it的泊松分布,则相邻两次事件的时间间隔T服从参数为i的指数分布。
Suppose that a failure in any event for t long time v (T) to the number of parameters for the distribution of it Poisson, is adjacent to the two event time interval T obeys the parameters for the distribution of I index。
解释:
Interpretation:
直接从泊松分布解释比较困难。因为泊松分布是二项分布在一定条件下的近似,所以我们看二项分布。
Directly from the Poisson distribution to explain difficult。
Because the Poisson distribution are the two distribution in a certain approximation, we look at two distribution。
设事件发生概率为p,则不发生概率为1-p。所谓“相邻两次事件”,即“在这两次事件之间没有发生事件”。
Set event probability for the P, not the probability for the 1-p。
The so-called "two adjacent event", namely "no events between the two events"。
按二项分布近似到泊松分布的过程,将相邻两次事件之间的时间间隔T分割为很多个小时间段,每段时长为λ,在每个小时间段内发生一次事件的概率为p,不发生概率为1-p。
According to the two distribution approximation to the Poisson distribution, will be between two adjacent event time interval T is divided into many small time, each time length λ, an event probability in each time period is p, not the probability for the 1-p
若在时间点t上发生了一次事件,那么:
If the t at a time there was an event, then:
在t与t+λ之间没有发生事件的概率为1-p,在t+λ与t+2λ之间发生了事件的概率为p,两次事件之间时间间隔为λ的概率为(1-p)p;
Probability events did not occur between T and t+ λ 1-p, the probability of events between t+ λ t+2 λ P and probability, the time interval between two events for lambda for (1-p)
在t与t+2λ之间没有发生事件的概率为(1-p)2,在t+2λ与t+3λ之间发生了事件的概率为p,两次事件之间时间间隔为2λ的概率为(1-p)2p;
Probability events did not occur between T and t+2 λ (1-p) is 2, the probability of events between t+2 λ and t+3 λ P, between the two event time interval for the probability of 2 λ (1-p) for
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嗯,这个就有点像指数分布了。
Well, this is a bit like the exponential distribution。收起