Estimation of parameters

Testing of hypophysis about independence of wear times for non-overlapping parts of an experimental specimen relates to the set of non-parametric statistics problems, which operate with infinitely many properties of the sample. That is why statistical verifying of this hypophysis is impossible for any large value of experimental data. The independence hypophysis is usually the object of believe until a case of its essential contradiction.

The direct way of data gathering

Traditional testing of wear at fixed time epochs sometimes is the uniquely possible under exploitation conditions of the technical product. Taking into account this fact, we investigate the problem of estimating the process parameters starting from the table of data, where random observation correspond to a priori fixed time epochs. In this connection we can meet two variants of data gathering: with restoration of the initial conditions (statical method), and without of such a restoration (dynamical method). Under the statical method one can consider values of wear in every circle of measurement as independent random values. For example, the testing device stops after a determinate time. The tested specimen is being taken out and weighted for determining of wear value, and then it is being established again for new testing and so on. In this case the one-dimensional distribution corresponding to a fixed time epoch contains all the information about the sample distribution. Some complications can arise for different time intervals between measurements because it gives not identical distributed members of the sample.

For the inverse gamma process, beginning at the point (0,0), the one-dimensional density can be found from formula (8). Thus for a space homogeneous process we have ft e—1 s (^s)ix-1 fX e—Yu

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