Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution

Abstract

Point and interval estimations are taken into account for a progressive first-failure censored left-truncated normal distribution in this paper. First, we derive the estimators for parameters on account of the maximum likelihood principle. Subsequently, we construct the asymptotic confidence intervals based on these estimates and the log-transformed estimates using the asymptotic normality of maximum likelihood estimators. Meanwhile, bootstrap methods are also proposed for the construction of confidence intervals. As for Bayesian estimation, we implement the Lindley approximation method to determine the Bayesian estimates under not only symmetric loss function but also asymmetric loss functions. The importance sampling procedure is applied at the same time, and the highest posterior density (HPD) credible intervals are established in this procedure. The efficiencies of classical statistical and Bayesian inference methods are evaluated through numerous simulations. We conclude that the Bayes estimates given by Lindley approximation under Linex loss function are highly recommended and HPD interval possesses the narrowest interval length among the proposed intervals. Ultimately, we introduce an authentic dataset describing the tensile strength of 50mm carbon fibers as an illustrative sample.

Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

“…But sometimes, it is not appropriate to use the symmetric function when an overestimate plays a crucial role compared with an underestimate, or vice versa. In this case, the asymmetric loss function is more appropriate (see Cai and Gui, 20 Kumara and Pandey 31 ). The most commonly used asymmetric loss function is general entropy loss (GEL) function.…”

“…In general cases, the conjugate prior distribution of unknown parameter is a preferred choice. If there is no definite prior information available for the unknown parameter, the prior distribution of the parameter is chosen as non‐informative prior (see Krishna, 8 zhang, 20 Dube, 21 Pandey, 30 and Kumari 31 ). From the likelihood function in Equation (), the joint conjugate priors for the unknown parameters $$\alpha ,\theta ,{\sigma }_1$$ and σ 2 cannot be obtained.…”

“…Due to the applicability of PFFC in life tests, this censoring scheme has attracted great attention from many scholars. Cai and Gui 20 studied the classical and Bayes inference for a left‐truncated normal distribution using PFFC samples. Dube et al 21 .…”

“…Due to the applicability of PFFC in life tests, this censoring scheme has attracted great attention from many scholars. Cai and Gui 20 studied the classical and Bayes inference for a left-truncated normal distribution using PFFC samples. Dube et al 21 considered the estimates of the unknown parameters and reliability characteristics of generalized inverted exponential distribution using PFFC samples.…”

Inferences for Generalized Pareto Distribution Based on Progressive First‐Failure Censoring Scheme

“…Many previous studies have discussed inference under a Pro-F-F-C scheme for different lifetime distributions, for example, Weibull by Wu and Kus ¸ [30], Burr Type XII by Soliman et al [31,32], Gompertz by Soliman et al [33], Lomax by Mahmoud et al [34], Compound Rayleigh by Abushal [35], Generalized Inverted Exponential by Ahmed [36], the Mixture of Weibull and Lomax by Mahmoud et al [37], and exponentiated Frechet by Soliman et al [38]. Recently, Cai and Gui [39] discussed the classical and Bayesian inference for a Pro-F-F-C lefttruncated normal distribution.…”