Abstract
A generalization of some well-known probability distributions (viz., Weibull, exponential, gamma, Maxwell, and Chi-square) is introduced using the concept of weighted probability distributions. The introduced model is named Kth-order equilibrium Weibull distribution (KEWD). Various properties of the new distribution are studied in detail. One of the important properties of KEWD is that its hazard rate shows increasing, decreasing, and constant behavior. It is also shown that the new model belongs to the log exponential family. Various ordering relations of the KEWD are studied in comparison with the baseline model, i.e. Weibull distribution. Parameters are estimated using the concept of the maximum likelihood estimation technique. Using the Anderson–Darling test statistic, a simulation study is carried out to analyze the asymptotic normality behavior of maximum likelihood estimators. The behaviors of bias and mean square error are observed with the increase in sample size. The applications of new distribution are illustrated through its fitting to some incorporated real-life data sets. Finally, a comparison is made between KEWD, its sub-models, and some other introduced extensions of Weibull distribution in terms of fitting using the Akaike information criterion (AIC).
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications in Statistics - Simulation and Computation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
