Zusammenfassung: When histograms are used instead of raw data to estimate parameters by the maximum likelihood method, data has an error distributed according to a regular distribution among the width of the histogram. This influence on the estimation of parameters is evaluated by the linearized error propagation rule. Covariance is in proportion to the width squared and in inverse proportion to the number of data. Even if the number of data is large, the precision is low for small normal distributions. In practice, an adequate width will be given by the shapes of the histograms.

Zusammenfassung: The statistical model for the Petersen method is a hypergeometric distribution. Approximation to a binomial distribution has been used, and the usual method for this binomial model is based on approximation to a normal distribution. The Bayesian statistical model for a binomial distribution, which assumes that the prior distribution of parameters is uniform, corresponds well with the conventional method. However, the Bayesian statistical method for a hypergeometric distribution which assumes the uniform prior distribution is not feasible. The prior distribution according to the inverse squared parameter is natural for this model. Beta function and zeta function are important to understand these methods. This model is simpler to understand and easier to calculate by micro-computer than the conventional method.