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This paper compares two point estimators of fraction defective of a normal distribution when both population parameters are unknown; the minimum variance unbiased estimator, &Fmacr;(χ), and the maximum likelihood estimator, &Fcirc;(χ). Using minimum mean squared error as a criterion, it is shown that the choice of estimator depends upon the true value of F(χ), and the sample size. In the domain .0005 ≤ F(χ) ≤ .50, the maximum likelihood estimator is generally superior even for small sample sizes, except for F(χ) less than about 0.01, or greater than 0.25. Furthermore, the bias in the m.l.e. is slight over much of the domain where this estimator has smaller mean squared error. As a practical solution to the estimation problem, it is suggested that the m.v.u.e. be calculated, and if this estimate is between 0.01 and 0.25, it should be replaced with the m.l.e. This combined estimator is shown to be nearly as efficient as the better of the m.v.u.e. and m.l.e. throughout the domain of F(χ). [ABSTRACT FROM AUTHOR]

A method is suggested for obtaining a multiple linear regression equation which permits the variance, as well as the mean, of normally distributed random variables, Y, to be a function of known constants X[sub 1] ... X[sub p]. The method is applicable to large samples, and yields an approximation of maximum likelihood estimates of regression coefficients, which may be used to construct confidence intervals for the parameters of the normal distribution and tolerance intervals for individual Y. A likelihood ratio test may be used to test this model against the usual homoscedastic least squares model. Two examples of this type of analysis on data from the literature are presented. [ABSTRACT FROM AUTHOR]