By Jfry KSmit
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Sampling Plan II: Assuming the first observation period begins at time zero, observe the renewal process at time and record the number of renewals in . Also record the time until the next renewal following time which will signal the start of a new observation period. Then after a period of time units, the number of renewals occurring in this second period is recorded. Record the time elapsed until the next renewal and the renewal epoch begins the following observations period, etc. The second sampling plan uses the additional information on the waiting time to start the next observation.
20). BASAWA Suppose the process is observed until the number of departures reaches a fixed value n. 28) Let nij be the number of transitions of Qt from i to j on the sample path, and , the vector of parameters for which estimators are being sought. 29) Depending on the form of the service time distribution, an explicit expression for the likelihood function can be written down and maximized in the usual manner to determine maximum likelihood estimates. The same general formulation holds when the service times are dependent.
11) the first integral represents the total demand during (0, t] and the second integral is the part of this demand that is not met. 6). 10) is the one with unit demand rate (that is, d(x)≡1), which arises also in the queueing system M/G/1 and single server queues with Poisson arrivals and static or dynamic priorities. In the queue M/G/1, the input X(t) of workload is a compound Poisson process, and Z(t) represents the remaining workload (virtual waiting time) at time t. In dam models the special cases of input include the gamma process, stable process with exponent 1/2 and the inverse Gaussian process.
Applied Statistics and the SAS Programming Language by Jfry KSmit