Bayesian and non-Bayesian estimations of truncated inverse power Lindley distribution under progressively type-II censored data with applications

Abstract

In this article, we introduce and study the truncated inverse power Lindley distribution. The aim is to transpose the remarkable flexibility of the two-parameter inverse power Lindley distribution to the interval [0,1]. The corresponding probability density function has the potential to be unimodal, decreasing, right-skewed, and heavy-tailed. On the other hand, the hazard rate function can be increasing, N-shaped, or U-shaped. These shapes’ versatility enables accurate representation and analysis of proportional or percentage data across a wide range of applications, such as survival analysis, reliability, and uncertainty modeling. Several statistical features, such as the mode, quantiles, Bowley’s skewness, Moor’s kurtosis, MacGillivray’s skewness, moments, inverse moments, incomplete moments, and probability-weighted moments, are computed. In practice, for the estimation of the model parameters from truncated data under the progressively type-II censoring scheme, the maximum likelihood, maximum product spacing, and Bayesian approaches are used. The Tierney–Kadane approximation and Markov chain Monte Carlo techniques are employed to produce the Bayesian estimates under the squared error loss function. We present some simulation results to evaluate these approaches. Four applications based on real-world datasets—one of them is on times of infection, the second is on failure times, and the other two are on the rate of inflation in Asia and Africa—explain the significance of the new truncated model in comparison to some reputed comparable models, such as the inverse power Lindley, Kumaraswamy, truncated power Lomax, beta, truncated Weibull, unit-Weibull, Kumaraswamy Kumaraswamy, and exponentiated Kumaraswamy models.

Classical and Bayesian estimation for Gompertz distribution under the unified hybrid censored sampling with application

“…This plan has previously been covered in several literary works, see, for example, those by Balakrishnan and Kundu, 3 Huang and Yang, 4 Habibi Rad and Izanlo, 5 Panahi and Sayyareh, 6 Jeon and Kang, 7 Sarkar and Tripathy, 8 and Dutta et al 9 Recently, many researchers have been interested in using different types of schemes using many lifetime models through many applications. For more details, see the works by Nassar et al, 10 Nassr and Elharoun, 11 Hassan et al, 12 Nassr and Azm, 13 El Azm et al, 14 Yousef et al, 15 Elgarhy et al, 16,17 Bantan et al, 18,19 Elbatal et al, 20 Shrahili et al, 21 Algarni et al, 22 Alotaibi et al, 23 Ahmadini et al, 24 Mohamed et al, 25 Abdelwahab et al, 26 Alyami et al, 27 Helmy et al, 28 Hassan and Nassr, 29,30 and Abd-Elfattah et al 31 The Gompertz distribution, first proposed by Benjamin Gompertz as a model for the distribution of income in Ref. 32, is considered to represent the underlying distribution in this study.…”

Reliability and the engineering applications of the generalized half-normal model via an adaptive progressive hybrid censored mechanism

“…The test stops at the time of the mth failure Xm:m:n, and at this point, all the remaining items are removed, i.e., Rm = n − m − ∑ m−1 i=1 Ri. Several publications on estimating the unknown parameters for various distributions under this censoring approach have recently appeared, see, for example, that of Balakrishnan et al, 6 Basak et al, 7 Ahmed, 8 Alotaibi et al, 9 Alotaibi et al, 10,11 and Elgarhy et al 12,13 Kundu and Joarder 14 proposed a progressive type-I hybrid censoring technique that has the same schematic representation as the P-II-C scheme but terminates testing at T * = min(T, Xm:m:n), where T is a fixed duration. The primary problem in this design is that the required sample size is random and may end up being quite small.…”