The Maximum Likelihood Estimate of the Non-Centrality Parameter of a Non-Central χ 2 Variate
非中心卡方变量非中心参数的最大似然估计
The maximum likelihood estimate for the non-centrality parameter of a non-central χ2 distribution with two degree of freedom is obtained. This estimate is expressed as a solution of an equation involving Bessel functions of order 0 and 1, of purely imaginary argument, both of which are tabulated. The derivation rests mainly on a lemma dealing with limit and monotonicity properties of a function representable as a quotient of two Bessel functions. An asymptotic result is also…