I have following sequence of 0-1 values where 1 represents arrival of something, and each 0 and 1 are measured in equal time unit (e.g. every hour). Below is an example of such sequence
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Above sequence contains 1 at positions
87, 89, 100, 349, 665, 669, 716, 723, 766, 921, 984, 1245, 1362, 1364, 1726, 1729, 1790, 1962, 2215, 2216
I found that statistical tests show that the null hypothesis that zeros and ones are occurring independently can not be rejected.
Next, I also tested if the waiting time to get 1 is memoryless through testing the null hypothesis of Exponential distribution with alternative as Weibull distribution.
Above test to study the memoryless property is strongly rejected.
I fail to interpret the results from above 2 tests. If memoryless property is rejected then shouldnt that the independence of 0/1 also be rejected?