The Gompertz-G family of distributions. (English) Zbl 1426.62057
Summary: We introduce and study some general mathematical properties of a new generator of continuous distributions with two extra parameters called the Gompertz-G generator. We present some special models. We investigate the shapes of the density and hazard functions and derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, and order statistics. Two bivariate extensions of this model are proposed. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the potentiality of the new class by means of two real data sets.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62G30 | Order statistics; empirical distribution functions |
| 62H10 | Multivariate distribution of statistics |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62B10 | Statistical aspects of information-theoretic topics |
Keywords:
generated family; Gompertz distribution; maximum likelihood; moment; order statistic; probability weighted moment; quantile function; Rényi entropy; bivariate extensionReferences:
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