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.

我们为两参数加权Lindley（WL）分布提出了新的闭式估计。这些新的估计器是从幂变换后的WL分布的似然方程得出的。它们的行为与最大似然估计器（MLE）非常相似，并实现了一致性和渐近正态性。数值结果表明，与现有的闭式估计器不同，新的估计器可与MLE一致地比较。另外，为了减少小样本情况下新估计量的偏差，我们基于近似Cox-Snell公式对新估计量应用偏差校正方法。我们的仿真研究表明，这种偏差校正方法可有效提高小样本性能。最后，我们给出三个真实的数据示例。