A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications

• Published in: Symmetry (Basel) 2023-07, Vol.15 (7), p.1396
• Main Authors: Elgarhy, Mohammed, Alsadat, Najwan, Hassan, Amal S., Chesneau, Christophe, Abdel-Hamid, Alaa H.
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Censored data (mathematics); Censorship; Datasets; Distribution (Probability theory); Entropy; entropy and extropy; Experiments; inverse Topp–Leone distribution; Markov chain Monte Carlo; Markov chains; Mathematical models; maximum likelihood and Bayesian estimations; maximum product spacing estimation; Monte Carlo method; Parameters; Probability; Probability density functions; progressive type-II censoring; Random variables; Skewed distributions; Statistical analysis
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym15071396

In this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distribution, to the bounded interval [0, 1]. The probability density function of the proposed truncated distribution has the potential to be unimodal and right-skewed, with different levels of asymmetry. On the other hand, its hazard rate function can be increasingly shaped. Some important statistical properties are examined, including several different measures. In practice, the estimation of the model parameters under progressive type-II censoring is considered. To achieve this aim, the maximum likelihood, maximum product of spacings, and Bayesian approaches are used. The Markov chain Monte Carlo approach is employed to produce the Bayesian estimates under the squared error and linear exponential loss functions. Some simulation studies to evaluate these approaches are discussed. Two applications based on real-world datasets—one on the times of infection, and the second dataset is on trading economics credit rating—are considered. Thanks to its flexible asymmetric features, the new model is preferable to some known comparable models.