Survival Analysis of Type-II Lehmann Fréchet Parameters via Progressive Type-II Censoring with Applications

Abstract

A new three-parameter Type-II Lehmann Fréchet distribution (LFD-TII), as a reparameterized version of the Kumaraswamy–Fréchet distribution, is considered. In this study, using progressive Type-II censoring, different estimation methods of the LFD-TII parameters and its lifetime functions, namely, reliability and hazard functions, are considered. In a frequentist setup, both the likelihood and product of the spacing estimators of the considered parameters are obtained utilizing the Newton–Raphson method. From the normality property of the proposed classical estimators, based on Fisher’s information and the delta method, the asymptotic confidence interval for any unknown parametric function is obtained. In the Bayesian paradigm via likelihood and spacings functions, using independent gamma conjugate priors, the Bayes estimators of the unknown parameters are obtained against the squared-error and general-entropy loss functions. Since the proposed posterior distributions cannot be explicitly expressed, by combining two Markov-chain Monte-Carlo techniques, namely, the Gibbs and Metropolis–Hastings algorithms, the Bayes point/interval estimates are approximated. To examine the performance of the proposed estimation methodologies, extensive simulation experiments are conducted. In addition, based on several criteria, the optimum censoring plan is proposed. In real-life practice, to show the usefulness of the proposed estimators, two applications based on two different data sets taken from the engineering and physics fields are analyzed.

Inference and physics applications of the logistic-exponential parameters using adaptive progressively hybrid censoring

“…This application provides an analysis of a real data set consisting of 30 successive values of precipitation (in inches) in Minneapolis/St Paul for March. This data collection was reported by Hinkley [40] and reexamined by mq -q q m --- Ghitany et al [41], Elshahhat et al [42], and Alotaibi et al [43]. Each point in the March precipitation data is multiplied by ten for convenience, see table 17.…”

Bayesian and non-bayesian inference for logistic-exponential distribution using improved adaptive type-II progressively censored data

“…An engineering application employing a real-life data set reported by Murthy et al [24] is analyzed to demonstrate how approaches suggested may be tailored to real phenomena. In recent time, Elshahhat et al [25] reanalyzed this RME data set for AT-II PCS following weightedexponential distribution. This data set which demonstrates the intervals between failures for thirty pieces of repairable mechanical equipment (RME) is given below: 0:11; 0:30; 0:40; 0:45; 0:59; 0:63; 0:70; 0:71; 0:74; 0:77; 0:94; 1:06; 1:17; 1:23; 1:23; 1:24; 1:43; 1:46; 1:49; 1:74; 1:82; 1:86; 1:97; 2:23; 2:37; 2:46; 2:63; 3:46; 4:36; 4:73:…”

“…An engineering application employing a real-life data set reported by Murthy et al [ 24 ] is analyzed to demonstrate how approaches suggested may be tailored to real phenomena. In recent time, Elshahhat et al [ 25 ] reanalyzed this RME data set for AT-II PCS following weighted-exponential distribution. This data set which demonstrates the intervals between failures for thirty pieces of repairable mechanical equipment (RME) is given below: Before proceeding with the analysis, it is important to determine whether the proposed model adequately fits the data.…”

Evaluations of Chris-Jerry Data Using Generalized Progressive Hybrid Strategy and Its Engineering Applications

“…In this part, we analyze real data representing the times 22 ball bearings (BBs) rotated before they stopped after one million rotations; see Table 15. Caroni [30] and Elshahhat et al [31] examined this dataset. To examine the superiority of the CJ model, using the BBs data set, the suggested CJ distribution will be compared to the XL, XG, M, L, and E lifetime models.…”