Zusammenfassung: BASIC programs to analyse the polymodal frequency distribution into normal distributions were studied and a Maximum-Likelihood program was compared with a Least-Squares program and its variations. The Maximum-Likehood method is the most suitable procedure for the problem. The X super(2) minimum method is more suitable than the Least-Squares method for normal data, but the latter is more suitable than the former for abnormal data which have a few separate parts at the end of a distribution. These methods are easy to apply for a good estimation. Parameters are stable where an obvious minimal value is recognized between neighboring distributions, but the confidence intervals of the parameters are larger than for the parts where it is not recognized.

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.