Parameter Estimation for Bivariate Mixed Lognormal Distribution

Abstract

Bivariate mixed lognormal distribution is a probability model used for representing rainfalls behavior at two monitoring stations. The paper discuss on the parameter estimation for bivariate mixed lognormal distribution in which all parameters are assumed to be unknown. Six cases were considered in the analysis and the parameters were estimated using the maximum likelihood. The optimal model was selected based on the minimum Akaike’s information criterion (AIC) from selected model. The analysis is run by using the rainfall data observed for the time period of 33 years (1975-2007) from Arau, Perlis with each of the other 7 nearby monitoring stations and 5 far distance stations. Among the 7 stations studied, 6 stations (87.5%) choose the same case model (M2) as the minimum AIC procedures. Meanwhile, 4 of the far distance stations choose the case M2 as the best fit case model.