Statistical modelling of rainfall data using modified Weibull distribution
Keywords:Fisher information, Instantaneous failures, Mixture distribution, Maximum likelihood estimator, Singular distribution at zero, Confidence interval, Weibull plot
This article presents the aspects of modeling rainfall data using a modified version of weibull distribution. This model takes care of those days reported with zero rainfall corresponding to the dry days (i.e., no rain day) during a season (in life testing context this situation is called instantaneous failures). We propose a modified weibull distribution as a suitable model to represent such situations by mixture of a singular distribution at zero and a two parameter weibull distribution. We derive Maximum Likelihood Estimates (MLE) of the parameters and their joint asymptotic distributions as well as that of the mean rainfall. Based on the above results a 95% confidence interval for the mean of the mixture distribution is obtained. The method is illustrated with actual measured data on rainfall from two stations namely, Jalgaon and Coimbatore divisions in India during a 10 year period from 1961 to 1970. Correspond to each year, the estimates of the parameters, average rainfall and confidence intervals are provided.
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