Lord Rayleigh, F.R.S. (1880) On the Resultant of a Large Number of Vibrations of the Same Pitch and of Arbitrary Phase. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 10, 73-78.
https://doi.org/10.1080/14786448008626893

has been cited by the following article:

• TITLE: A New Weighted Rayleigh Distribution: Properties and Applications on Lifetime Time Data

  AUTHORS: Shakila Bashir, Mujahid Rasul

  KEYWORDS: RD, ARD, MOM, ML, Bayesian

  JOURNAL NAME: Open Journal of Statistics, Vol.8 No.3, June 28, 2018

  ABSTRACT: Rayleigh distribution (RD) has wide applications in many real life situations especially life testing, reliability analysis, medicines etc. In this paper a new weighted Rayleigh distribution named area-biased Rayleigh distribution (ARD) is introduced. Some mathematical properties of the (ARD) including cumulative distribution function, moments, skewness, kurtosis, median, mode, entropy, reliability measures as survival function and hazard function have been derived. Parameter of the ARD is estimated by method of moments (MOM), maximum likelihood (ML), and Bayesian. Properties of the estimators are developed. It is proved that the ML estimator attains the Cramer Rao lower bound. Applications of the ARD provided for some life time data sets. Kolmogorov Smirnov (K-S) test statistics is applied to check the good fit of the model.