A Mathai-type Multivariate Nakagami-$m$ Distribution: Density, Closed-form Estimators, and Asymptotic Efficiency

2026-09-13

AI Summary

本文提出了一种新的多变量Nakagami-m分布，并通过一种渐近有效闭式估计器解决了其最大似然估计不可闭式表达的问题。

Abstract

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.

Problem

• multivariate Nakagami-m distribution
• closed-form expression
• maximum likelihood estimator

Innovation

• Mathai-type construction
• closed-form estimator
• asymptotic efficiency