Parameter Estimations for Generalized RayleighDistribution under Progressively Type-I IntervalCensored Data

Abstract

In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods

Estimating the parameters of an inverse Weibull distribution under progressive type-I interval censoring

“…In this work, the author analyzed a one-parameter exponential distribution under this censoring, and obtained classical estimates for the unknown parameter. Statistical inference under progressive type-I interval censoring has been further discussed by Ashour and Afify (2007) for exponentiated Weibull family, Ng and Wang (2009) for Weibull distribution, Lio et al (2011) for generalized Rayleigh distribution, Xiuyun and Zaizai (2011) for gamma distribution and Chen and Lio (2010) and Chen et al (2013) for generalized exponential distribution. Bayesian inference under this censoring has also been discussed by various researchers, see for instance, Lin and Lio (2012) for Weibull and generalized exponential distributions, Peng and Yan (2013) for generalized exponential distribution and Pradhan and Gijo (2013) for lognormal distribution.…”

Planning Step-Stress Life Tests for the Generalized Rayleigh Distribution Under Progressive Type-II Censoring with Binomial Removals

“…If q= 1, the GRD reduces to the traditional Rayleigh distribution. As indicated by [2][3][4][5], the GRD has been studied in many papers. Also, Surles and Padgett [6] showed that the two-parameter GRD can be used quite effectively in modeling strength data and also modeling general lifetime data.…”

Bayesian estimation of the shape parameter of generalized Rayleigh distribution under non-informative prior

“…In 2001, two parameter Burr Type X distribution was introduced by Surles and Padgett [14]. Abdel-Hady [1], Kundu and Raqab [8] and Lio, Chen and Tsai [9] prefer to call this distribution GRD; this name will be adopted in this work. For α>0 and λ>0, the two-parameter GRD will be denoted by GRD(α, λ) and its cumulative distribution function is given by:…”

“…It is used as a model for wind speed and is often applied to wind driven electrical generation. It can also be used in modelling strength and lifetime data (we refer an interested reader to, Kundu & Raqab [8], Lio, Chen and Tsai [9], Samaila and Cenac [13] and Surles and Padgett [14]). The graph of the GRD is shown in figure 1 for different shape parameter values.…”