Department of Mathematics, Al-Lith University College, Umm Al-Qura University, Mecca, Saudi Arabia.
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.
Comput Intell Neurosci. 2022 Apr 30;2022:4822212. doi: 10.1155/2022/4822212. eCollection 2022.
The LINEX loss function, which climbs exponentially with one-half of zero and virtually linearly on either side of zero, is employed to analyze parameter analysis and prediction problems. It can be used to solve both underestimation and overestimation issues. This paper explained the Bayesian estimation of mean, Gamma distribution, and Poisson process. First, an improved estimator for is provided (which employs a variation coefficient). Under the LINEX loss function, a better estimator for the square root of the median is also derived, and an enhanced estimation for the average mean in such a negatively exponential function. Second, giving a gamma distribution as a prior and a likelihood function as posterior yields a gamma distribution. The LINEX method can be used to estimate an estimator using posterior distribution. After obtaining , the hazard function and the function of survival estimators are used. Third, the challenge of sequentially predicting the intensity variable of a uniform Poisson process with a linear exponentially (LINEX) loss function and a constant cost of production time is investigated using a Bayesian model. The APO rule is offered as an approximation pointwise optimal rule. LINEX is the loss function used. A variety of prior distributions have already been studied, and Bayesian estimation methods have been evaluated against squared error loss function estimation methods. Finally, compare the results of Maximum Likelihood Estimation (MLE) and LINEX estimation to determine which technique is appropriate for such information by identifying the lowest Mean Square Error (MSE). The displaced estimation method under the LINEX loss function was also examined in this research, and an improved estimation was proposed.
LINEX 损失函数在零的一半处呈指数增长，在零的两侧几乎呈线性增长，用于分析参数分析和预测问题。它可以用于解决低估和高估问题。本文解释了均值、Gamma 分布和泊松过程的贝叶斯估计。首先，提供了一个改进的均值估计量（使用变异系数）。在 LINEX 损失函数下，还推导出了一个更好的中位数平方根估计量，并增强了在这种负指数函数中对平均均值的估计。其次，给出 Gamma 分布作为先验，似然函数作为后验，得到 Gamma 分布。可以使用 LINEX 方法对后验分布进行估计，得到一个估计量。得到 后，使用风险函数 和生存函数的估计。第三，使用贝叶斯模型研究了使用线性指数（LINEX）损失函数和恒定生产成本的均匀泊松过程的强度变量的顺序预测问题。提供 APO 规则作为点最优规则的近似。使用 LINEX 作为损失函数。已经研究了各种先验分布，并评估了贝叶斯估计方法与平方误差损失函数估计方法的比较。最后，通过确定最小均方误差（MSE）来确定哪种技术适用于此类信息，比较最大似然估计（MLE）和 LINEX 估计的结果。本文还研究了 LINEX 损失函数下的位移估计方法，并提出了一种改进的估计方法。
