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<p>The unit gamma distribution is suitable for modeling random variables in the unit interval (0,1). However, in practical situations, the data may contain zeros and/or ones with non-null probability. In such cases, appropriate distributions are necessary to model variables restricted to (0, 1], [0, 1) or [0,1] intervals. This paper proposes the inflated unit gamma distribution, presents its main properties and derives expressions to obtain the maximum likelihood estimators of the parameters. Additionally, we conduct a numerical evaluation to evaluate the performance of point estimates, confidence intervals and hypothesis tests in finite sample sizes. According to the results, the inflated unit gamma distribution presents satisfactory performance and proves to be a potential competitor for the inflated beta and inflated Kumaraswamy distributions. Furthermore, the proposed inflated distribution estimates its own mean, rather than the mean of the continuous distribution, as it is commonly done in most inflated distributions discussed in the literature. Finally, we present and discuss two empirical applications to illustrate the applicability of the proposed distribution and compare it with other inflated distributions in the literature.</p>

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Zero-One-Inflated Unit Gamma Distribution and its Application to Basic Sanitation Data

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • Camila Ribeiro da Silva,
  • Tarciana Liberal Pereira,
  • Luiz Medeiros Araujo Lima–Filho,
  • Paulo José Duarte–Neto

摘要

The unit gamma distribution is suitable for modeling random variables in the unit interval (0,1). However, in practical situations, the data may contain zeros and/or ones with non-null probability. In such cases, appropriate distributions are necessary to model variables restricted to (0, 1], [0, 1) or [0,1] intervals. This paper proposes the inflated unit gamma distribution, presents its main properties and derives expressions to obtain the maximum likelihood estimators of the parameters. Additionally, we conduct a numerical evaluation to evaluate the performance of point estimates, confidence intervals and hypothesis tests in finite sample sizes. According to the results, the inflated unit gamma distribution presents satisfactory performance and proves to be a potential competitor for the inflated beta and inflated Kumaraswamy distributions. Furthermore, the proposed inflated distribution estimates its own mean, rather than the mean of the continuous distribution, as it is commonly done in most inflated distributions discussed in the literature. Finally, we present and discuss two empirical applications to illustrate the applicability of the proposed distribution and compare it with other inflated distributions in the literature.