Abstract
This study discusses the posterior estimation for the parameters of the Burr type II distribution (BIID). The informative and noninformative priors along with different loss functions have also been assumed for the posterior estimation. The applicability of the proposed distribution has also been discussed. The modeling capability of the proposed model has been compared with seven classes of the lifetime distributions using real data. The generalizations of Weibull, exponential, Rayleigh, gamma, log normal, Pareto, Maxwell, Levy, Laplace, inverse gamma, Gompertz, chi-square, inverse chi-square, half normal, and log-logistic distributions have been considered for the comparison. The comparison has been made based on different goodness-of-fit criteria, such as Akaike information criteria (AIC), Bayesian information criteria (BIC), and Kolmogorov-Smirnov (KS) test. Based on the results from the study, it can be suggested that the BIID can efficiently replace commonly used lifetime distributions and their modifications. The results under this model were comparable with different conventional/modified distributions having up to six parameters.
Highlights
Lifetime distributions are very useful in reliability analysis
This section starts with the simulation study for the proposed Bayes estimates using different sample sizes, different parametric values, different priors, and different loss functions
We have proposed the Bayesian analysis for the parameters of the Burr type II distribution (BIID) assuming different priors and loss functions (SELF, Precautionary Loss Function (PLF), Quadratic Loss Function (QLF), and Entropy Loss Function (ELF)) to estimate the parameters of the proposed distribution
Summary
Lifetime distributions are very useful in reliability analysis. There are many conventional models available in literature to model life data. A class of life distribution including twelve models was introduced by Burr [1] From this family of distribution, the Burr type III (BIIID), Burr type X (BXD), and Burr type XII (BXIID) have been frequently used for lifetime analysis. BIID has not received much attention in modeling life datasets The analysis of such deprived distribution is always of interest for research for exploring their hidden properties and applications. Feroze and Aslam [6] obtained the ML estimates for the parameters of the Burr type V distribution (BVD) under left censored samples. Ahmad et al [13] obtained Bayes estimates and maximum likelihood estimates for the BXD based on doubly type II censored. Rastogi and Tripathi [18] considered the problem of estimating reliability function of BXIID on the basis of a censored type II sample. 0.005855 the numerical integrations were employed to obtain the said estimates numerically
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