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On families of beta- and generalized gamma-generated distributions and associated inference

On families of beta- and generalized gamma-generated distributions and associated inference,10.1016/j.stamet.2008.12.003,Statistical Methodology,K. Zo

On families of beta- and generalized gamma-generated distributions and associated inference   (Citations: 7)
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A general family of univariate distributions generated by beta random variables, proposed by Jones, has been discussed recently in the literature. This family of distributions possesses great flexibility while fitting symmetric as well as skewed models with varying tail weights. In a similar vein, we define here a family of univariate distributions generated by Stacy’s generalized gamma variables. For these two families of univariate distributions, we discuss maximum entropy characterizations under suitable constraints. Based on these characterizations, an expected ratio of quantile densities is proposed for the discrimination of members of these two broad families of distributions. Several special cases of these results are then highlighted. An alternative to the usual method of moments is also proposed for the estimation of the parameters, and the form of these estimators is particularly amenable to these two families of distributions.
Journal: Statistical Methodology , vol. 6, no. 4, pp. 344-362, 2009
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    • ...One may ask: when we choose one over the other? We will answer this question for arbitrary parent distribution by following a method proposed by Zografos and Balakrishnan 18...

    Saralees Nadarajahet al. A new family of lifetime models

    • ...Recently, Zografos and Balakrishnan 1 have introduced a new family of distributions generated by gamma random variables...

    Miroslav M. Ristićet al. The gamma-exponentiated exponential distribution

    • ...Recently, Zografos and Balakrishnan 1 have introduced a new family of distributions generated by gamma random variables...

    Miroslav M. Ristićet al. The gamma-exponentiated exponential distribution

    • ...New, broad families of probability distributions have been proposed and studied in the recent literature (see, for example, [1], [2], [3] and references therein)...

    K. Zografoset al. Generalized families of univariate distributions

    • ...This representation of X helps to generate random numbers from (1) while the case α = β = 1 corresponds to the wellknown quantile function representation X = F −1 (U ), where U ∼ U (0, 1), which is used in order to generate data from a distribution F . The family (1) has been recently studied by Zografos and Balakrishnan [24]...
    • ...Name of the distribution Authors / Year Beta-Normal Eugene et al. [6] Beta-Logistic Brown et al. [5] and Olapade [20] Beta-Frechet Nadarajah and Gupta [17] Beta-Gumbel Nadarajah and Kotz [18] Beta-Exponential Nadarajah and Kotz [19] Beta-Gamma Kong et al. [12] Beta-Weibull Lee et al. [13] and Zografos [23] Beta-Pareto Akinsete et al. [3] Beta-Power Zografos and Balakrishnan [24] Beta-Generalized Half Normal Pescim et al. [22] ...
    • ...kα x kα−1 � 1 − (θx) k � β−1 ,0 24])...
    • ...This permits the development of an alternative to the method of moments estimation procedure, as it is described in Zografos and Balakrishnan [24]...
    • ...bution F and the parent density f . This term plays a key role to introduce a test for discriminating between the members of the GBG-II distribution, in a manner similar to that which is developed in Zografos and Balakrishnan [24]...

    Kostas Zografos. Generalized Beta Generated-II Distributions

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