Lately, a New Transmuted Logistic-exponential (NTLE) distribution was introduced and studied as an extension of the Logistic-Exponential Distribution (LED) with wider applicability in lifetime modelling. However, the maximum likelihood estimates (MLE) of NTLE are not in closed form, and the consistency of the estimates was not examined. Furthermore, some other important properties of NTLE, namely the Shannon entropy, Rényi entropy, stochastic ordering, mode, stress-strength reliability measure, residual life functions (mean and reverse), incomplete moments, Bonferroni and Lorenz curves are yet to be derived. Motivated by this, we derived and studied these important properties and evaluated the performance of ten estimation methods (Maximum Likelihood, Moments, Least Squares, Weighted Least Squares, Maximum product of Spacings, Anderson-Darling, Cramer-von Mises, percentile estimation, and Maximum Goodness-of-Fit methods) for NTLE parameters via Monte Carlo simulation using bias, mean square error, and root mean square error as evaluation criteria. Real-life infectious mortality data fitted to the distributions showed that NTLE has a better fit compared to its base distributions (Exponential and Logistic-Exponential). This finding contributes valuable insights for researchers and practitioners when selecting the appropriate estimation methods, especially for NTLE and some similar distributions in non-closed form.

翻译：近期，一种新的转换逻辑-指数分布被提出并作为逻辑-指数分布的扩展进行研究，在寿命建模中具有更广泛的适用性。然而，该分布的最大似然估计没有闭合形式，且估计的一致性尚未得到检验。此外，该分布的其他重要性质——包括香农熵、雷尼熵、随机序、众数、应力-强度可靠性度量、残存寿命函数（均值与逆函数）、不完全矩、邦弗朗尼曲线与洛伦兹曲线——仍有待推导。受此驱动，我们推导并研究了这些重要性质，并通过蒙特卡洛模拟评估了十种估计方法（最大似然估计、矩估计、最小二乘估计、加权最小二乘估计、最大间距积估计、安德森-达林估计、克拉默-冯·米塞斯估计、百分位数估计及最大拟合优度估计）在该分布参数估计中的性能，以偏差、均方误差和均方根误差作为评估标准。对实际传染病死亡率数据的拟合表明，相较于其基础分布（指数分布与逻辑-指数分布），该分布具有更好的拟合效果。这一发现为研究者和实践者在选择合适估计方法时提供了有价值的参考，尤其适用于该分布及其他类似非闭合形式分布。