A new method for generating families of continuous distributions. (English) Zbl 1302.62026
Summary: In this paper, a new method is proposed for generating families of continuous distributions. A random variable \(X\), “the transformer”, is used to transform another random variable \(T\), “the transformed”. The resulting family, the \(T-X\) family of distributions, has a connection with the hazard functions and each generated distribution is considered as a weighted hazard function of the random variable \(X\). Many new distributions, which are members of the family, are presented. Several known continuous distributions are found to be special cases of the new distributions.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62B10 | Statistical aspects of information-theoretic topics |
| 60E05 | Probability distributions: general theory |
Keywords:
hazard function; Pearson system; beta-family; generalized distribution; entropy; Shannon entropyReferences:
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