Zusammenfassung: Leslie's removal method, which is used to estimate the initial population size and the removal ratio simultaneously, is modeled in terms of the product of binomial distributions. The approximation of these binomial distributions to the standard normal distribution presents a new method which has no bias for estimators. This is an improvement over the maximum likelihood method and the likelihood ratio test, and is essentially equivalent to a standard goodness-of-fit test. The confidence region on the 2-dimensional plane defined by the initial population size and the removal ratio gives each confidence interval. This region is defined by the chi-square distribution with 2 degrees of freedom.

Zusammenfassung: In mathematics, the age-length key method is an estimating method for the ratio of each distribution in a mixture of distributions. Although the maximum likelihood method is the principle of this estimation, this model is a nonlinear model with a restrictive condition. At first, Hasselblad solved this model by using a new iteration method with a computer. Although his method was regarded as the steepest descent method or EM algorithm, it is proved to be an application of Lagrange's indeterminate multiplier method to the iteration method. Nowadays, there are other useful algorithms of optimization, especially Marquardt's method, for this estimation.

Zusammenfassung: A microcomputer system that weighs and measures fish and records the data on a computer file was tested at two hatcheries. The device produced fairly accurate lengths and might save labor and reduce transcription errors.