Analyzing recurring event data is crucial in clinical, epidemiological, and a wide range of other fields, requiring consideration of the interdependence among events within individuals and potential variability in event likelihood across different individuals. This paper introduces a comprehensive suite of models aimed at addressing the gap in parametric frailty models designed for recurrent events. The proposed models encompass five distinct baseline intensities and integrate gamma, inverse Gaussian, and positive stable frailty distributions. Parameter estimation is optimized for maximizing the marginal log-likelihood and accommodates both right-censored and potentially left-truncated data. Model selection is facilitated through the Aikake Information Criterion (AIC) and Bayesian Information Criterion (BIC). Simulation studies assess the computational algorithm and the efficacy of the proposed models. The models' performance is further demonstrated through the analysis of a dataset focusing on recurrent outcomes of phototherapies. Among the proposed models, the one based on a gamma frailty and Weibull baseline intensity stands out with a lower AIC and BIC, establishing it as an enhanced and robust framework for capturing underlying patterns in eczema datasets. The estimates within this model include baseline intensity parameters, incidence relative risk for potential covariates, and the frailty's variance. Beyond capturing the effects of risk factors, the frailty's variance indicates the presence of unobserved heterogeneity in recurrent events not accounted for by the risk factors in the model. The extensive evaluation, involving simulation studies and real-world data analysis, underscores the utility and effectiveness of these parametric frailty models, making a significant contribution to the field of survival analysis