1957/06/01 by M. C. K. Tweedie · 6 citations
Physics and Astronomy · Computer Science · #Statistical Mechanics and Entropy #Bayesian Methods and Mixture Models #Gaussian Processes and Bayesian Inference
paper · pdf · doi:10.1214/aoms/1177706964
A report is presented on some statistical properties of the family of probability density functions exp \lbrack -λ(x - μ)2/2μ2x\rbrack\lbrackλ/2π x3\rbrack1/2 for a variate x and parameters μ and λ, with x, μ, λ each confined to (0, ∞). The expectation of x is μ, while λ is a measure of relative precision. The chief result is that the ml estimators of μ and λ have stochastically independent distributions, and are of a nature which permits of the construction of an analogue of the analysis of variance for nested classifications. The ml estimator of μ is the sample mean, and for a fixed sample size n its distribution is of the same family as x, with the same μ but with λ replaced by λ n. The distribution of the ml estimator of the reciprocal of λ is of the chi-square type. The probability distribution of 1/x, and the estimation of certain functions of the parameters in heterogeneous data, are also considered.