Mathai型多元Nakagami-$m$分布：密度、闭式估计量与渐近效率
A Mathai-type Multivariate Nakagami-$m$ Distribution: Density, Closed-form Estimators, and Asymptotic Efficiency
- Konkuk University（建国大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种具有闭式密度的多元Nakagami-$m$分布，并基于一步修正构造渐近有效的闭式估计量，其性能接近数值最大似然估计且优于初始估计量。
AI中文摘要：
在本研究中，我们提出了一种新的多元Nakagami-$m$分布，其联合概率密度函数具有完全闭式表达式。所提出的密度是基于独立伽马随机变量的部分和，采用Mathai型构造推导而得。对于该分布，最大似然估计量不存在闭式形式。为解决这一局限，我们通过对一个$\sqrt{n}$相合初始估计量应用一步修正，开发了一种渐近有效的闭式估计量。蒙特卡洛模拟表明，所提出的估计量在性能上与数值计算的最大似然估计量几乎相同，同时始终优于闭式初始估计量。一项真实数据应用进一步说明了其实用价值。
英文摘要：
In this study, we propose a novel multivariate Nakagami-$m$ distribution whose joint probability density function admits a fully closed-form expression. The proposed density is derived using a Mathai-type construction based on the partial sums of independent gamma random variables. For this distribution, the maximum likelihood estimator is not available in the closed form. To address this limitation, an asymptotically efficient closed-form estimator is developed by applying a one-step refinement to a $\sqrt{n}$-consistent initial estimator. Monte Carlo simulations demonstrate that the proposed estimator achieves a performance nearly identical to that of the numerically computed maximum likelihood estimator, while consistently outperforming the closed-form initial estimators. A real-data application further illustrates its practical utility.
