IMPACT OF STATE SIZE ON CONVERGENCE RATE OF MARKOV CHAIN WITH APPLICATION TO RAINFALL VARIABILITY IN MAKURDI. NIGERIA

Rainfall variability is an important component of the climate system and can be effectively modelled using Markov chains. This study compares the convergence behaviour of two-state and three-state Markov chain models using daily rainfall data from Makurdi, Nigeria. Both models were found to be ergodic, ensuring unique stationary distributions. Mixing time, measured using Total Variation Distance (TVD), was employed to assess the speed of convergence under a uniform initial distribution. The two-state model converged to its stationary distribution after 24 days, while the three-state model required 31 days, indicating slower convergence with increased state complexity. Both models showed a higher longrun probability of dry conditions, with the two-state model estimating stationary probabilities of 57% for dry days and 43% for wet days. By comparing mixing times across different state-space models, this study provides insights into rainfall persistence and supports improved agricultural planning, drought assessment, and rainfall forecasting.