The McDonald inverted beta distribution |
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| Authors: | Gauss M Cordeiro Artur J Lemonte |
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| Institution: | 1. Departamento de Estatística, Universidade Federal de Pernambuco, Recife/PE, Brazil;2. Departamento de Estatística, Universidade de São Paulo, São Paulo/SP, Brazil;1. Hepia, University of Applied Sciences of Western Switzerland, Earth Nature Environment Institute, Route de Presinge 150, 1254 Jussy (GE), Switzerland;2. INRA, UMR 0042 Carrtel, F-74203 Thonon, France;3. Fédération de Haute-Savoie pour la Pêche et la Protection du Milieu Aquatique, Le Villaret, 2092 route des Diacquenods, 74370 St-Martin Bellevue, France;1. Department of Statistics, St. Anthony’s College, Shillong, Meghalaya, India;2. Department of Quantitative Health Sciences, Cleveland Clinic, Cleveland, OH, USA;3. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA;1. Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany;2. Aalto Science Institute, Aalto University, PO Box 11000, FI-00076 Aalto, Finland;3. Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz, Germany |
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| Abstract: | We introduce a five-parameter continuous model, called the McDonald inverted beta distribution, to extend the two-parameter inverted beta distribution and provide new four- and three-parameter sub-models. We give a mathematical treatment of the new distribution including expansions for the density function, moments, generating and quantile functions, mean deviations, entropy and reliability. The model parameters are estimated by maximum likelihood and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models. |
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