GBVE分布的参数估计

叶慈南

系统科学与数学 ›› 1995, Vol. 15 ›› Issue (1) : 39-049.

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PDF(451 KB)
系统科学与数学 ›› 1995, Vol. 15 ›› Issue (1) : 39-049. DOI: 10.12341/jssms09130
论文

GBVE分布的参数估计

    叶慈南
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ESTIMATORS OF PARAMETERS OF GBVE DISTRIBUTION

    YE CI-NAN
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摘要

设二元随机变量(X,Y)的生存函数为可.把它称作GBVE(θ1,θ2,δ).本文采用把元件和系统(串联)的定时截尾寿命试验数据综合起来进行统计分析的方法,研究GBVE(θ1,θ2,δ)中参数的估计及其性质.在θ1=θ2=θ的情况下给出了(θ,δ)的极大似然估计证明了具有强相合性和渐近正态性.在无θ1=θ2限制时给出了(θ1,θ2,δ)的矩法估计(θ1,θ2,θ3,δ),证明了同样具有强相合性和渐近正态性.

Abstract

Let the survival function of two-dimensional random variables(X, Y) be F(x,y) ~ exp{-[(x /θ1),1/δ + (y/θ2)1/δ]δ}, 0< x,y <∞, 0<δ≤1.0<δθ1,θ2< ∞.We refer to it as GBVE(θ1,θ2,δ).In this paper, using both time-truncated life testing data of components and series systems, we study the estimators and their properties of parameters of GBVE (θ,θ1,δ). In the case of θ1=θ2=θ, we give the maximum likelihood estimator (θL,δL) of (θ,δ) and prove that (θ,δ) has strong consistency and asymptotic normality. In the case without the restriction of θ1 = θ2, we give the moment type estimator(θ1,θ2,δ) of (θ1,θ2,δ), and prove that (θ1,θ2,δ) has strong consistency and asymptotic normality, too.

关键词

二元指数 / 寿命试验 / 参数估计 / 渐近性质

Key words

Bivariate exponential / life test / parameter estimation / asymptoticproperties.

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叶慈南. GBVE分布的参数估计. 系统科学与数学, 1995, 15(1): 39-049. https://doi.org/10.12341/jssms09130
YE CI-NAN. ESTIMATORS OF PARAMETERS OF GBVE DISTRIBUTION. Journal of Systems Science and Mathematical Sciences, 1995, 15(1): 39-049 https://doi.org/10.12341/jssms09130
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