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Potential changes in hydro-meteorological events have been causing mass damage to the economy and lives. Among several other factors, the progression of climate change over a long time is expected to cause non-stationarity in annual maximum rainfall. Understanding the characteristics of annual maximum rainfall series is crucial for coastal cities as they are highly vulnerable due to the greatly varying weather patterns. In this paper, we propose stationary and non-stationary methods to model the effect of non-stationarity on the differing duration of annual maximum rainfall and demonstrate the impacts on nine coastal cities spread across the Arabian Sea and Bay of Bengal stretch of India. The Bayesian inference parameter estimation technique was used. It was found that while stationary models often fit well for longer-duration rainfall, non-stationary models often best fit the short duration. [ABSTRACT FROM AUTHOR]