| چکیده انگلیسی مقاله |
Introduction: Although geometric distribution, which is a special case of Negative Binomial (NB) distribution, also belongs to the discrete family of distributions, little attention has been paid to modeling count data with the geometric distribution. There are many real-life phenomena that follow the geometric distribution with a constant probability of first success. However, in practice, the probability of the first success may vary from trial to trial, making simple geometric models unsuitable for modeling such data. In this paper, assuming that the probability of the first success follows a Beta distribution, we developed a Beta-geometric distribution and Beta-geometric regression for modeling the count data that follow the geometric distribution and illustrated the suitability of the model through application to the count data on time to first antenatal care (ANC) visit.
Methods: The statistical properties of the Beta-geometric distribution are discussed. The estimation of the parameters of the distribution using the method of moments, maximum likelihood estimation (MLE) method, and Bayesian estimation approach are provided. Based on the Beta-geometric distribution, we developed a new Beta-geometric regression model for analyzing count data that follow the geometric distribution. The goodness of fit of the derived model has been tested using real data on time to the first ANC visit.
Results: Beta-geometric distribution has a simple form for its probability mass function (pmf), and is flexible in capturing both underdispersion and overdispersion that may present in count data. It was found that the proposed Beta-geometric regression model fit the count data on the first ANC visit better than simple geometric distribution or Negative Binomial distribution.
Conclusion: Unlike the Poisson or Negative Binomial distribution, Beta-geometric distribution does not need an additional parameter to accommodate underdispersion or overdispersion and thus could be a flexible choice for analyzing any count data. |