There is a probability distribution of a discrete random variable "x" (is given below), which the probability that the distribution stay constant (with a tolerance of 5%) with the passage of the time t = 365. when the number of measurements (sample size) in each period t is is 50-250.
x1 = 3; P1 = 0,0079
x2 = 6; P2 = 0,2371
x3 = 9; P3 = 0,3557
x4 = 12; P4 = 0,2570
x5 = 15; P5 = 0,1265
x6 = 18; P6 = 0,0158
distribution remaining constant
over time ! Stationary distribution!
Dear Andrii,
The description of the problem gives unsufficient information and the question is posed unclearly. One can guess only that each day you measure 50 - 200 times some quantities with possible values 3,6,. . .,18 and that the daily frequencies, which you call probabilities, vary arround the listed values plus/minus 5%. Possibly, you should perform a test of the stationarity of your process. For this you need some introductory model of possible perturbation. The simplest example could be the forllowing:
The random variables X1,X2,X3, . . . X365 are iid (independent identically distributed) on the set of possible values {3,6,9,12,15,18}., additionaly, that the measurements each day are mutually independent, too.
In this case the simplest is a suitable chi^2 Pearson test verifying that all the samples come from the same distribution. Further hints require more details, e.g.:
what are the changes within a singe day?
is it possible to assume independence of the variables X1,X2, . . . X365?
are the obervations within one day dependent on the hour?
Regards
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