New closed-form estimators for weighted Lindley distribution

• Published in: Journal of the Korean Statistical Society Vol. 50; no. 2; pp. 580 - 606
• Main Authors: Kim, Hyoung-Moon, Jang, Yu-Hyeong
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.06.2021; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Mathematics and Statistics; Research Article; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; Maximum likelihood estimator; Closed-form estimators; Bias correction; Asymptotic distribution; Weighted Lindley distribution
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1007/s42952-020-00097-y

We propose new closed-form estimators for two-parameter weighted Lindley (WL) distribution. These new estimators are derived from likelihood equations of power transformed WL distribution. They behave very similarly to maximum likelihood estimators (MLEs) and achieve consistency and asymptotic normality. Numerical results show that, unlike existing closed-form estimators, the new estimators are uniformly comparable to MLEs. In addition, to reduce biases of the new estimators in the case of small samples, we apply a bias-correction method to the new estimators, based on the approximate Cox-Snell formula. Our simulation studies indicate that this bias-correction method is effective in enhancing small-sample performance. Finally, we present three real data examples.