Modeling of Rainfall Quantity and Incidence: A Tweedie Distribution Approach

Abstract

Introduction

This study tried to explore a non-traditional statistical distribution from the Tweedie family of distributions, particularly the Poisson-Gamma Distribution, that can simultaneously model the probability of rainfall quantity which is continuously containing precise zero outcomes and rainfall incidence which is discrete because it has only two states. It aimed to widen perspectives, insights, and knowledge in the field of applied statistics and its application to meteorology. This study also served as a guide and blueprint in making the same research paper on other regions in the Philippines.

Methods

The rainfall data from the year 2000 to 2016 of Dagupan City, Philippines was utilized. The predictors or covariates used were the sine and cosine terms wherein m=1,2, ,4,...,12 are the months in a year. Descriptive statistics were employed. To determine the model-based from Poisson-Gamma Distribution used in model fitting, parameter estimates were determined using the Tweedie distribution. Fitting the model to the data required the estimation of many parameters. Model validation was performed using Bootstrapping Technique.

Results

The monthly rainfall data in Pangasinan from 2000-2016 revealed that it has wet months from May to October and dry months from November to April. The mean-variance relationship was computed and the result shows an approximately linear relationship. Using the sine and cosine predictors, the significance of the computed coefficients was tested using the Wald Chi-Square test and it shows that both the sine and cosine terms have significant coefficients. Using the estimated model, the estimated values of the coefficients and the dispersion parameter, the mean rainfall quantity for a specific month was derived.

Discussions

Pangasinan belongs to Type I climate according to PAGASA Climate Map Classification. The performance of the model in predicting rainfall quantity is good because it resembles the actual observed data based on the MAPE score. The formula in computing the probability of zero rainfall occurrence for a month, based on the reparametrization of the parameters and found that it could predict the probability of zero rainfall well for all months except for the months of January to April.