Open AccessNew extensions of Rayleigh distribution based on inverted-Weibull and Weibull distributions
Author(s) -
Mohammad Smadi,
Mahmoud H. Alrefaei
Publication year - 2021
Publication title -
international journal of power electronics and drive systems/international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
eISSN - 2722-2578
pISSN - 2722-256X
DOI - 10.11591/ijece.v11i6.pp5107-5118
Subject(s) - weibull distribution , kurtosis , rayleigh distribution , rayleigh scattering , estimator , quantile , rayleigh wave , statistics , mathematics , computer science , statistical physics , probability density function , physics , optics , wave propagation
The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models.