Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

Abstract

In life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. Lately, an adaptive progressive type-II hybrid censoring scheme is suggested to enhance the efficiency of the statistical inference. By utilizing this scheme, this paper seeks to investigate classical and Bayesian estimations of the Dagum distribution. The maximum likelihood and Bayesian estimation methods are considered to estimate the distribution parameters and some reliability indices. The Bayesian estimation is developed under the assumption of independent gamma priors and by employing symmetric and asymmetric loss functions. Due to the tough form of the joint posterior distribution, the Markov chain Monte Carlo technique is implemented to gather samples from the full conditional distributions and in turn obtain the Bayes estimates. The approximate confidence intervals and the highest posterior density credible intervals are also obtained. The effectiveness of the various suggested methods is compared through a simulated study. The optimal progressive censoring plans are also shown, and number of optimality criteria are explored. To demonstrate the applicability of the suggested point and interval estimators, two real data sets are also examined. The outcomes of the simulation study and data analysis demonstrated that the proposed scheme is adaptable and very helpful in ending the experiment when the experimenter’s primary concern is the number of failures.

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

“…Recently, this sampling plan is used in various applied sciences. Among several works in the literature, see Panahi and Moradi [10], Elshahhat and Nassar [11], Ateya et al [12], Elshahhat et al [13], Nassar et al [14], Alotaibi et al [15], Mohammed et al [16], Alotaibi et al [17,18]. The main feature of these works is the investigation of some estimation issues for some lifetime models considering classical and Bayesian procedures.…”

“…Similarly, we can formulate the joint posterior distribution of μ and θ using the SF in (16) and the joint prior distribution given by (21) as follows…”

“…In this context, 'possible schemes' refers to the various options of (R 1 ,K,R m ) for fixed sample size n, fixed effective sample size m and fixed threshold time T. In recent years, the statistical literature has paid an enormous amount of attention to selecting an optimal censoring method for different problems. See, for instance, Ng et al [29], Kundu [30], Pradhan and Kundu [31] and Mohammed et al [32]. Here, we investigate the optimal censoring scheme based on both of the classical estimation methods.…”

Inferences of inverted gompertz parameters from an adaptive type-ii progressive hybrid censoring

“…where C is a constant and q is a parametric vector. Different researches based on the proposed censoring have been conducted by several authors in the literature; for example, see Nassar and Abo-Kasem [6], Mohie El-Din et al [7], Ateya and Mohammed [8], Liu and Gui [9], Elshahhat and Nassar [10], Panahi and Asadi [11], Helu and Samawi [12], El-Sherpieny et al [13], Alotaibi et al [14], Mohammed et al [15], and references cited therein.…”

Introduction to the Special Issue in Symmetry Titled “Symmetry in Statistics and Data Science”

“…The ninth article, "Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications" by Mohammed et al [9], seeks to investigate classical and Bayesian estimations of the Dagum distribution based on the adaptive progressive type II hybrid censoring scheme. Two real data sets are also looked at to show how the suggested point and interval estimators can be used.…”