Comparison ML-and MM- estimates fixed duration of the dead time MAP-flow of events
The Markovian arrival process (MAP-flow) with the intensity representing a piecewise-constant random process X(t) with two states is considered: X(t) = X 1 or X(t) = X 2 (X 1 > X 2). The dwell time of the process X(t) in the i-th state is random variable with exponential distribution function Fj = 1 - e , i = 1, 2. At the moment of termination of the i-th state of the process X(t) the following situations are possible, each of which proceeds instantly: 1) process X(t) transits from the i-th state to the i-th state, and an event of flow in the i-th state occurs; the joint probability of this situation is P(X i ^ X, ,1) = Pj (X г- | X i) i = 1, 2; 2) process X(t) transits from the i-th state to the j-th state, and an event of the flow occurs; the joint probability of the situation is P(X i ^ X j ,1) = Pj(X j | X i), i, j = 1, 2; i Ф j; 3) process X(t) transits from the i-th state to the j-th state, and no event of the flow occurs; the joint probability of the situation is P(X i ^ X ; ,0) = P0(X j | X i), i, j = 1,2; i Ф j. Thus, Pj (X , | X ,) + P,(X ; | X, ) + P0(X ; | X, ) = 1, i, j = 1, 2; i Ф ]' X1 1 0 2 X1 = ||D 0 | D Ц. 1 1 1 1 1 1 2 1 2 0 1 2 2 2 1 1 2 2 1 2 2 The elements of the matrix D1 are intensities of transitions from state with occurrence of an event. Non-diagonal elements of the matrix D0 are the intensities of transitions from state to state, but no event occurs. Diagonal elements of the matrix D0 are the intensities of the exit of the process X(t) from the states taken with the opposite sign. Under these assumptions, X(t) is the hidden Markov process. A comparison of the estimates of fixed dead time obtained (observations obtained as a result of a simulation model of the flow of events MAP) by the method of maximum likelihood and the method of moments. D =
Keywords
MAP-поток,
непродлевающееся мертвое время,
метод максимального правдоподобия,
оценка максимального правдоподобия,
метод моментов,
оценка метода моментов,
MAP-flow fixed dead time,
the method of maximum likelihood,
maximum likelihood estimation,
method of moments,
the evaluation method of momentsAuthors
| Gortzev Alexandr M. | Tomsk State University | gam@mail.fpmk.tsu.ru |
| Solovev Alexandr A. | Tomsk State University | sizal19@mail.ru |
Всего: 2
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