THE APPLIED OF FUNCTIONAL DATA ANALYSIS TO COMPARISON 100 TIMES SIMULATED MONTHLY RAINFALL USING SOME TWO PARAMETERS DISTRIBUTION

Three probability models of mothly rainfall such as Gamma, Weibulland Log Normal distribution are evaluated in terms of their ability to reproduce the mean statistics derived from 100 times simulation of monthly rainfall in the Pekanbaru City, Indonesia. One of the important studies is to investigate and understand the simulate mean monthly rainfall patterns that occur throughout the year. To identify the pattern,  it  requires  a  rainfall  curve  to  represent  monthly  observation  of  rainfall  received  during  the year. Functional data analysis (FDA) methods are capable to convert discrete data into a function that can represent the rainfall curve and as a result, try to describe the hidden patterns of the rainfall. This study is focused on investigating 100 curve average monthly rainfall simulatated  by three different quantile functions  using  the  FDA.  The  mean  and  standard  deviation  of  FDA  for  average  monthly precipitation are obtained. Through these two statistics a  the confidence interval curves of the mean curve are presented represent 95% pointwise confidence intervals. In this study, most of the monthly average rainfall from the actual data were around the FDA mean and the monthly average rainfall was within the FDA confidence interval. In this study, 100 times monthly rainfall simulations using the quantile function of thegamma and log normal distributions found that the mean  FDA can capture most of the mean monthly rainfall from historical data, and  within the FDA interval. The contradictory results shown by the monthly rainfall simulations using the Weibull distribution, most of the monthly average  rainfall  historical  data  cannot  be  captured  by  the  FDA  mean  and  are  outside  the  FDA confidence interval. Based on the Mean Absolute Error (MAE) value of the average monthly rainfall of historical data and the monthly average of the FDA, it can be concluded that the gamma distribution can produce simulated rain better than the log normal distribution