Geodesic
Models of Alternating Renewal Process at Discrete Time
Serdica Mathematical Journal, Tome 27 (2001) no. 2, pp. 115-130.

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We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.
Keywords: Time Series, Alternating Renewal Process, Sojourn Time Laws, Persistence 
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Bousseboua, Moussedek; Lazhar Rahmani, Fouad. Models of Alternating Renewal Process at Discrete Time. Serdica Mathematical Journal, Tome 27 (2001) no. 2, pp. 115-130. http://geodesic.mathdoc.fr/item/SMJ2_2001_27_2_a2/