Statistical inference for doubly geometric process with exponential distribution

The geometric process is widely applied as a stochastic monotone model in many practical applications since its introduction. However, it sometimes does not satisfy some requirements the real-world due to limitations. For this reason, proposed new which called doubly process. In of process, estimation problem associated with arises naturally. study, statistical inference for considered by assuming that distribution first interarrival time has an exponential distribution. maximum likelihood method used estimate parameters and parameter joint estimators obtained. A simulation study presented evaluate small sample performance different values. Finally, three real-world-data sets are illustrate applicability methods.