Estimation of the Parameters in the Double-periodic Model
DOI:
https://doi.org/10.17713/ajs.v27i1&2.529Abstract
The periodic behavior of environmental conditions and its effects on waiting time is of principal interest in a number of modeling problems. Dimitrov and Khalil (1992) have used a constructive approach to introduce a new class of probability distributions which exhibits the periodic behavior of environmental conditions in time and the random occurrence of some events on each time period. Further, the authors discussed some physical and probabilistic properties of the new class. In a more recent work, Dimitrov et al. (1996) investigated a somewhat more complicated case of modeling the waiting time to occurrence of a random event governed by random environment with driving periodic or double periodic structure. In this contribution, we will make use of these important results to find estimators of the parameters in the double periodic model, where after a given number of time periods, say m, the conditions start to repeat, the same as from the origin. Phenomena of this type appear in a series of environmental, maintenance and financial processes. In particular, we expect that investigators working in modelingenvironmental evolution with periodic behavior will find our new results useful.
References
R. Barlow and F. Proschan. Statistical theory of reliability and life testing. 2nd ed., Holt Rinehart and Wilson, 1991.
B. Dimitrov and Z. Khalil. A new class of probability distributions for modelling environmental evolution with periodic behavior. Environmetrics, 3(4):447-464, 1992.
B. Dimitrov, Z. Khalil, and M.A. El-Saidi. On probability distributions with accumulating failure rates in periodic random environment. Environmetrics, 7(4):17-26, 1996.
R.V. Hogg and A.T. Craig. Introduction to Mathematical Statistics. 5th ed., Prentice Hall, 1995.
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