Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution

Abstract

This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.

Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data

“…. , m. Due to the complicated expressions of (10) and (11), the MLEs cannot be computed in explicit forms. Accordingly, numerical iterative techniques must be performed to calculate the wanted estimates.…”

“…Under the assumption of APE distribution for lifetime observation, Salah [9] studied the estimation of the APE distribution using progressively Type-II censored data. Salah et al [10] investigated the APE distribution using Type-II hybrid censored samples. Alotabi et al [11] investigated the maximum likelihood and Bayesian estimates (BEs) of the APE distribution under progressively Type-II censored data.…”

Statistical Analysis Based on Progressive Type‐I Censored Scheme from Alpha Power Exponential Distribution with Engineering and Medical Applications

“…Using some simplifications, we can substitute equations ( 1) and (2) to equation (4) to get MLE and its information matrix for the APED's unknown parameters. e likelihood function in this scenario is provided by…”

“…Salah [3] studied parameters estimation of APED under progressive Type-II censored scheme (PCS-Type II) using the MLE. Salah et al [4] considered parameter estimation of APED under Type-II hybrid censored scheme (HCS-Type II) using the MLE and expectation maximizations algorithm. Also, they evaluated the estimated reliability and hazard functions.…”

Best Prediction Method for Progressive Type-II Censored Samples under New Pareto Model with Applications

“…Recently, several authors are interested in studying parameter inference of different distributions under progressive Type-II censoring scheme (PC) (see, for example, Kundu [8], Pradhan and Kundu [9], Maurya et al [10], and Bdair et al [11]). In addition, inference with other censoring schemes appeared in literature with different lifetime models, such as hybrid Type-I progressive censoring, adaptive Type-II progressive censoring, Type-II hybrid censoring, and others (see, for example, Bdair and Haj Ahmad [12]; Haj Ahmad et al [13]; Salah et al [14] Almetwally et al [15]; and Sabry et al [16]). Still there is much space for more work with different censoring schemes under new generalized models.…”