A Research Project submitted in partial fulfillment for the award of masters of science degree in applied statistics in the school of pure and applied sciences of Meru University of Science and Technology

Rainfall and temperature series and their corresponding extreme events impact heavily on the performance of a county's economy especially in a developing county like Kenya, which relies on rained agriculture. Such extremes when not analyzed and solved, have led to lots of uncertainties amongst stakeholders.These processes were analyzed to study the evolution of their mean variability.In particular, this study sort to model the Temporal Rainfall Patterns in different Zones in Kenya Considering Temperature Trends as indicators of the rainfall variations. In achieving this objective,two broad statistical approaches were used, one based on inference on the entire series to predict the mean amount of rainfall using the maximum and minimum temperatures and the other on modeling the extreme event processes.Data from different counties in Kenya regarding rainfall and temperature was obtained.The study then came up with zones dependent on rainfall using cluster analysis,fitted Poisson, Quasi-Poisson and Negative-Binomial models. Using the AIC criterion, the best model that could be used to explain the variability of rainfall patters in these Zones as maximum and minimum temperatures changed were identified. Finally,GPD model using POT methods were used to study the distribution of the extreme seasons in the Zones.It was realized in the end that the Negative Binomial glm model was the best fit for the seven identified zones while POT coupled with mean residual life (mean excess function) fitted the GPD model to the extreme seasons and accordingly, discussions on the same have been provided.