Abstract
We introduce a new distribution, called the logit exponentiated power exponential, defined on the unit interval. Explicit expansions are derived for its moments. Also, we propose a regression based on this distribution with two systematic components, which can provide better fits than the beta and simplex regressions. Its parameters are estimated by maximum likelihood. Some simulations investigate the accuracy of the estimates. The usefulness of the new models is proved by means of three real data sets.
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Appendix A: Shapes
Appendix A: Shapes
Figure 1 shows some shapes of the density (2) that include well-known distributions. These plots reveal that the logit-EPE density is very flexible, see, Fig. 9.
Plots of the logit-PE(\(\mu\), \(\sigma =0.30\), \(\nu =1.5\)) (solid line) and logit-EPE(\(\mu\), \(\sigma =0.30\), \(\nu =1.5\), \(\tau\)) (dotted line) densities for some values. a \(\tau =0.10\). b \(\tau =0.25\). c \(\tau =0.50\). d \(\tau =0.85\). e \(\tau =2.00\). f \(\tau =5.00\)
Plots of the logit-PE(\(\mu =0.50\), \(\sigma\), \(\nu =1.5\)) (solid line) and logit-EPE(\(\mu =0.50\), \(\sigma\), \(\nu =1.5\), \(\tau\)) (dotted line) densities for some values. a \(\tau =0.10\). b \(\tau =0.25\). c \(\tau =0.50\). d \(\tau =0.85\). e \(\tau =2.00\). f \(\tau =5.00\)
Plots of the logit-PE(\(\mu =0.50\), \(\sigma =0.20\), \(\nu\)) (solid line) and the logit-EPE(\(\mu =0.50\), \(\sigma =0.20\), \(\nu\), \(\tau\)) (dotted line) densities for some values. a \(\tau =0.10\). b \(\tau =0.25\). c \(\tau =0.50\). d \(\tau =0.85\). e \(\tau =2.00\). f \(\tau =5.00\)
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Prataviera, F., Batista, A.M., Ortega, E.M.M. et al. The Logit Exponentiated Power Exponential Regression with Applications. Ann. Data. Sci. 10, 713–735 (2023). https://doi.org/10.1007/s40745-021-00347-8
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DOI: https://doi.org/10.1007/s40745-021-00347-8