Handbook of Nonparametric Statistics

A sample is thought to be the result of mixing a random sample of size N ₁ from a p-variate normal population with mean and covariance matrix Σ with an independent random sample size N ₂ from a p-variate normal population with mean and covariance matrix Σ. It is wished to identify the population from which each observation has come and to estimate the parameters N ₁, N ₂, , and Σ. The paper discusses the application of the method of moments and the maximum likelihood method to the solution of this problem. The methods are illustrated by a numerical example.     

Handbook of Nonparametric Statistics

To search for an optimum in a large search space, Wu, Mao, and Ma suggested the sequential elimination of levels (SELs)-method to find an optimal setting. Genetic algorithms (GAs) can be used to improve on this method. To make the search procedure more efficient, new ideas of forbidden array and weighted mutation are introduced. Relaxing the condition of orthogonality, GAs are able to accommodate a variety of design points, which allows more flexibility and enhances the likelihood of getting the best setting in fewer runs, particularly in the presence of interactions. The search procedure is enriched by a Bayesian method for identifying the important main effects and two-factor interactions. Illustration is given with the optimization of three functions, one of which is from Shekel's family. A real example on compound optimization is also given.     

Introduction to Business Statistics

Confidence intervals based on the maximum likelihood estimators are given for the location and scale parameters of the Double Exponential distribution. These intervals are obtained by determining the distribution of the pivotal quantities ( – θ)/ and /σ. Exact distributions are determined for n = 3 and n = .5, and approximate distributions are provided for larger n. The asymptotic distributions are also given and the accluacy of these approximations are investigated. The powers of the associated tests of hypotheses are given and tolerance limits for the population are also provided. Some possible applications are indicated.