Statistical modeling of daily rainfall occurrences

In this paper, likelihood‐based inference procedures for discrete point process models are developed, and a new family of discrete point process models for daily rainfall occurrences is proposed. The model, which is termed a Markov Bernoulli process, can be viewed as a sequence of Bernoulli trials with randomized success probabilities. Contained within the family of Markov Bernoulli models are Markov chain and Bernoulli trial models. Asymptotic properties of maximum likelihood estimators of Markov Bernoulli model parameters are derived. These results provide the basis for assessing standard errors and correlation of parameter estimators and for developing likelihood ratio tests to choose among Markov Bernoulli, Markov chain, and Bernoulli trial models. Inference procedures are applied to a data set from Washington, D.C.