Let {Tn } be a renewal process in R＋ representing the successive arrival times of some natural events. We studied this process by using a record process approach under the assumption that the interarrival times T,, =...Let {Tn } be a renewal process in R＋ representing the successive arrival times of some natural events. We studied this process by using a record process approach under the assumption that the interarrival times T,, = Tn, - Ta-1, n = 1, 2...are exponentially i.i.d （independent and identically distributed）. The goal is to test that the first observed events are sporadic events. For testing the hypothesis ＂sporadic＂ we used the non-parametric test based on the probability distribution of the statistic of the number of records N, among{Xx }k-1= where Xk = （ΔTk）-1. We showed that it is independent of the cumulative distribution of the observations and that it is exactly calculated for each n. We illustrated this statistic on a simulated trajectory and we compared it with descriptive smoothing methods. We studied an application to a data set as storms in France and US.展开更多
文摘Let {Tn } be a renewal process in R＋ representing the successive arrival times of some natural events. We studied this process by using a record process approach under the assumption that the interarrival times T,, = Tn, - Ta-1, n = 1, 2...are exponentially i.i.d （independent and identically distributed）. The goal is to test that the first observed events are sporadic events. For testing the hypothesis ＂sporadic＂ we used the non-parametric test based on the probability distribution of the statistic of the number of records N, among{Xx }k-1= where Xk = （ΔTk）-1. We showed that it is independent of the cumulative distribution of the observations and that it is exactly calculated for each n. We illustrated this statistic on a simulated trajectory and we compared it with descriptive smoothing methods. We studied an application to a data set as storms in France and US.
