Abstract
Geometric process (GP) is widely used as a stochastic monotone model in many practical applications since its introduction. However, its scope is still limited. Due to this limitation, Wu, 2018 proposes a new stochastic process named as doubly geometric process (DGP). After defining a new stochastic process, estimation problem of the model parameters arises naturally. In this paper, the statistical inference problem for the DGP is considered when the distribution of the first inter-renewal time is assumed to be an exponential distribution. The model parameters of the DGP and the parameter of distribution are estimated by using the maximum likelihood (ML) method. The asymptotic distributions of the ML estimators are obtained. Finally, a Monte Carlo simulation study is carried out to evaluate the performance of the estimators.
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