Abstract
In this paper, we develop a generator to propose new continuous lifetime distributions. Thanks to a simple transformation involving one additional parameter, every existing lifetime distribution can be rendered more flexible with our construction. We derive stochastic properties of our models, and explain how to estimate their parameters by means of maximum likelihood for complete and censored data, where we focus, in particular, on Type-II, Type-I and random censoring. A Monte Carlo simulation study reveals that the estimators are consistent. To emphasize the suitability of the proposed generator in practice, the two-parameter Fréchet distribution is taken as baseline distribution. Three real life applications are carried out to check the suitability of our new approach, and it is shown that our extension of the Fréchet distribution outperforms existing extensions available in the literature.
Highlights
The modeling and analysis of lifetime phenomena is an important aspect of statistical work in a wide variety of scientific and technological fields
While their approach only allows modulating the shape of distributions in a fixed way, ours is more flexible since it contains the extra shape parameter λ to regulate the transformation
This is why, besides classical maximum likelihood estimation, we show how to estimate the parameters of our new family of distributions when the data are censored
Summary
Peer Review History: PLOS recognizes the benefits of transparency in the peer review process; we enable the publication of all of the content of peer review and author responses alongside final, published articles. Data Availability Statement: All relevant data are within the paper and its Supporting Information files.
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