The nonhomogeneous Poisson process with covariate effects

Regression models that include covariate effects in a nonhomogeneous Poisson process (NHPP) are considered in this dissertation. These models can be applied in diverse areas such as repairable systems and recidivism problems. Examples of covariates in an NHPP model for repairable systems include temperature, humidity and stress. Examples of covariates included in the model for a recidivism problem are gender, age and number of previous incarcerations.;Accelerated time and proportional intensity models are used to include covariate effects in this dissertation. They are analogous to accelerated life and proportional hazards models that are widely used in survival analysis. Least squares methods are used to estimate the regression coefficients in the accelerated time and proportional intensity models. Maximum likelihood parameter estimates for accelerated time models are derived. Goodness-of-fit tests that check the adequacy of accelerated time and proportional intensity models are developed. The results of parameter estimation of the proposed method are compared to other methods with respect to mean square error and bias. A split model is generalized to accommodate the split population in a recidivism model. Data sets of failure times of repairable systems and tumor occurrence times of female rats are studied by the proposed methods. Variate generation algorithms for nonhomogeneous Poisson process with time dependent covariates are developed.