Marinho Pedro R D, Bourguignon Marcelo, Silva Rodrigo B, Cordeiro Gauss M
Departamento de Estatística, Universidade Federal da Paraíba, Cidade Universitária, s/n, 58051-900 João Pessoa, PB, Brazil.
Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Lagoa Nova, 59078-970 Natal, RN, Brazil.
An Acad Bras Cienc. 2019;91(1):e20180480. doi: 10.1590/0001-3765201920180480. Epub 2019 Apr 8.
In this paper, we introduce a new three-parameter distribution by compounding the Nadarajah-Haghighi and geometric distributions, which can be interpreted as a truncated Marshall-Olkin extended Weibull. The compounding procedure is based on the work by Marshall and Olkin 1997. We prove that the new distribution can be obtained as a compound model with mixing exponential distribution. It can have decreasing, increasing, upside-down bathtub, bathtub-shaped, constant and decreasing-increasing-decreasing failure rate functions depending on the values of the parameters. Some mathematical properties of the new distribution are studied including moments and quantile function. The maximum likelihood estimation procedure is discussed and a particle swarm optimization algorithm is provided for estimating the model parameters. The flexibility of the new model is illustrated with an application to a real data set.
在本文中，我们通过将纳达拉贾 - 哈格希分布与几何分布复合，引入了一种新的三参数分布，它可被解释为截断的马歇尔 - 奥尔金扩展威布尔分布。复合过程基于马歇尔和奥尔金1997年的工作。我们证明了新分布可作为具有混合指数分布的复合模型得到。根据参数值，它可以具有递减、递增、倒浴盆形、浴盆形、恒定以及先递减后递增再递减的失效率函数。研究了新分布的一些数学性质，包括矩和分位数函数。讨论了最大似然估计过程，并提供了一种粒子群优化算法来估计模型参数。通过应用于一个实际数据集说明了新模型的灵活性。
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