Abstract
In this article, Maximum likelihood estimates for the shape and scale parameters of two-parameter Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-Maximization (EM) algorithm. A simple algorithm discussed in [2-3] is used for generating progressive type-II censored samples. Based on this censoring scheme, approximate asymptotic variances are derived and used to construct approximate confidence intervals of the parameters. The performance of these two maximum likelihood estimation algorithms is compared in terms of simulation results of root mean squared error (RMSE) and the coverage rates. Simulation results showed that in nearly all the combination of simulation conditions the estimators based on the EM algorithm have less root mean squared error (RMSE) and narrower widths of confidence intervals compared to those obtained using the NR algorithm. Finally, an illustrative example with real-life data sets is provided to illustrate how maximum likelihood estimation using the two algorithms works in practice.
Highlights
The two-parameter Rayleigh distribution is a particular case of a Weibull distribution widely used in reliability theory and life testing
The distribution has attracted several researchers as it occurs in different forms including one-parameter Rayleigh distribution, and twoparameter Burr type X distribution known as the Generalized Rayleigh distribution
Since the MLEs of the shape and scale parameters of the two-parameter Rayleigh distribution cannot be obtained in the explicit form, we propose the use of the NR and the EM algorithms to compute the MLEs
Summary
The two-parameter Rayleigh distribution is a particular case of a Weibull distribution widely used in reliability theory and life testing. Rayleigh [25] introduced this distribution in connection with a problem in acoustics. Rayleigh distribution has a nice relation to other distributions including Chi-Square and most extreme value distributions. The hazard function of this distribution increases with an increase in time. The distribution has attracted several researchers as it occurs in different forms including one-parameter Rayleigh distribution, and twoparameter Burr type X distribution known as the Generalized Rayleigh distribution. According to Surles and Padgett, the two-parameter Rayleigh distribution is an extreme value distribution that is effective in modeling general life data [26]
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