Statistical Inference of Burr–Hatke Exponential Distribution with Partially Accelerated Life Test under Progressively Type II Censoring

Abstract

In this paper, estimations of the parameter and acceleration factor of the Burr–Hatke exponential distribution in partially accelerated life tests under progressively type II censoring are investigated. By using typical maximum likelihood methods and the Bayesian method, point estimations of the distribution parameter and the acceleration factor are obtained. Based on the asymptotic normality and Delta method, approximate confidence intervals are established using the Fisher information matrix. The confidence intervals of the percentile bootstrap method are also evaluated. Comprehensive simulation tests are conducted to evaluate the estimations effects. A real dataset is studied by constructing a Burr–Hatke exponential model and analyzing the practicality and utility of parameter estimation.

New Generalized Nadarajah Haghighi Distribution: Characterization and Applications

“…Applicability and flexibility of the proposed NGNH model can be demonstrated numerically and graphically by using two real data sets. The fit of NGNH model is compared with other model fits such as (i) Nadarajah Haghighi distribution (NH) (Nadarajah and Haghigh (2011)), (ii) inverted Nadarajah Haghighi (INH) (Tahir, Cordeiro, Ali, Dey and Manzoor (2018)), (iii) Power inverted Nadarajah Haghighi (PINH), (iv) weighted Nadarajah Haghighi (WNH), (v) transmuted Inverted Nadarajah Haghighi (TINH) (Toumaj, Mirmostatae and Hamedani (2021)), (vi) Exponential (Exp) and (vii) two parameter Burr Hatke Exponential (2BHE) (Gao and Gui (2023)) distributions represented as…”