Abstract

Background: Modeling against non-normal data a challenge for theoretical and applied scientists to choose a lifetime model and expect to perform optimally against experimental, reliability engineering, hydrology, ecology, and agriculture sciences, phenomena. Method: We have introduced a new G class that generates relatively more flexible models to its baseline and we refer to it as the new modified Lehmann Type – II (ML–II) G class of distributions. A list of new members of ML–II-G class is developed and as a sub-model the exponential distribution, known as the ML-II-Exp distribution is considered for further discussion. Several mathematical and reliability characters along with explicit expressions for moments, quantile function, and order statistics are derived and discussed in detail. Furthermore, plots of density and hazard rate functions are sketched out over the certain choices of the parametric values. For the estimation of the model parameters, we utilized the method of maximum likelihood estimation. Results: The applicability of the ML–II–G class is evaluated via ML–II–Exp distribution. ML–II–Exp distribution is modeled to four suitable lifetime datasets and the results are compared with the well-known competing models. Some well recognized goodness–of–fit including -Log-likelihood (-LL), Anderson-Darling (A*), Cramer-Von Mises (W*), and Kolmogorov-Smirnov (K-S) test statistics are considered for the selection of a better fit model. Conclusion: The minimum value of the goodness–of–fit is the criteria of a better fit model that the ML–II–Exp distribution perfectly satisfies. Hence, we affirm that the ML–II–Exp distribution is a better fit model than its competitors.

Highlights

  • Over the past two decades, the growing attention of researchers towards the development of new G families has explored the remarkable characteristics of baseline models

  • A new modified Lehmann Type–II (ML–II) G class of distributions accompanied by a table of some special models is proposed and developed in A new modified Lehmann Type – II–G Class of distributions

  • We develop a new G class, known as a modified Lehmann Type–II (ML–II) G class of distributions

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Summary

Conclusion

The minimum value of the goodness–of–fit is the criteria of a better fit model that the ML–II–Exp distribution perfectly satisfies. Keywords Lehmann Type – II Distribution; Exponential Distribution; Hazard Rate Function; Moments; Rényi Entropy; Maximum Likelihood Estimation, Simulation

Introduction
À eÀηxγ
À αð1 À qÞβ1 ð1 À αÞð1 À qÞβ1
17. Rényi A
23. Balakrishnan N
26. El-Alosey AR
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