Three parameter Transmuted Rayleigh distribution with application to Reliability data

Abstract

This research introduces the three parameter transmuted Rayleigh distribution with an application to fatigue fracture data. Using the quadratic rank transmutation map method proposed by Shaw et al. [25] we develop the three parameter transmuted Rayleigh distribution. This research also introduces the new class of weighted Rayleigh distribution by using Azzalini [2] method. Some structural properties of the new distribution are derived such as moments, incomplete moments, probability weighted moments, moment generating function, entropies, mean deviation and the kth moment of order statistics. The parameters of the proposed model are estimated using the maximum likelihood estimation and obtain the observed information matrix. The potentiality of the proposed model is illustrated using fatigue fracture data.

Keywords

• 2P-Rayleigh distribution; weighted Rayleigh distribution; moment estimation; order statistics; maximum likelihood estimation.