Conclusion

Abstract

In this monograph, we presented a comprehensive in-depth study of the power Poisson processes $\mathcal {E}_{+}$ and $\mathcal {E}_{-}$. These Poisson processes are defined over the positive half-line $\left( 0,\infty \right)$, and are governed by power intensity functions. Specifically: the power Poisson process $\mathcal {E}_{+}$ is characterized by the intensity function $\lambda _{+}\left( x\right) =c\epsilon x^{\epsilon -1}$ ($x>0$), and the power Poisson process $\mathcal {E}_{-}$ is characterized by the intensity function $\lambda _{-}\left( x\right) =c\epsilon x^{-\epsilon -1}$ ($x>0$); the coefficient c and the exponent $\epsilon$ of these intensity functions are positive parameters.