
Akamine, T. (1993). A new standard formula for seasonal growth of fish in population dynamics (Vol. 59).
Zusammenfassung: This formula is based on the Richards formula, which includes wellknown growth formulae, and is invariant for allometry. It is expanded by exchanging the independent variable from time to its function, in other words the cumulative water temperature. This standard formula includes the method of substituting values for the cumulative water temperature into the time term, the mathematical model of adding sine functions to the time term, and switched growth rate models. This standard model is given by general theory, which makes the character of parameters clear and helps to analyze the growth formula statistically.
Schlüsselwörter: Fisch, wachstum, statistik, modell, population, theorie



Akamine, T. (1990). An interval estimation of Leslie's method in removal methods.
Zusammenfassung: Leslie's method in removal methods is modeled into the joint of the binomial distributions. An interval estimation of p (removal ratio) and n (initial population size) based on the null hypothesis for p and n is easily obtained by the approximation of each binomial distribution to the normal distribution. The confidence region on the (p, n) plane is easily obtained by microcomputers. The maximum likelihood method for a point estimation and the convenient method on the curves of partial maximum likelihood for an interval estimation are also presented.
Schlüsselwörter: Fisch, statistik, binominal, population, basic, listing, modell, methode



Akamine, T. (1989). An interval estimation for the Petersen method using Bayesian statistics.
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 microcomputer than the conventional method.
Schlüsselwörter: Bayesian, binominal, basic, listing, methode, theorie, algorithmus



Akamine, T. (1989). An interval estimation for extraction using Bayesian statistics.
Zusammenfassung: The statistical model for extraction is a binomial distribution. The conventional method for employing this binomial model is based on approximation to a normal distribution. The Bayesian statistical method, which assumes that the prior distribution of parameters is uniform, is preferable to the conventional method, and two theorems demonstrate that this model corresponds well with the conventional method. Furthermore, this model is simpler to understand and easier to calculate by microcomputer than the conventional method.
Schlüsselwörter: Bayesian, normalverteilung, binominal, statistik, theorie, algorithmus, listing, basic



Akamine, T. (1988). Estimation of parameter for Richards model.
Zusammenfassung: Akamine's (1986) BASIC program by Marquardt's method was rewritten for Richards model and its expanded model by the periodic function. For 0.9 similar to 1.1 the “LOG” function is corrected by Taylor series. Data estimated to be negative are cut off. AIC judges the effect of adding n to the parameters. Richards model is not so important in practice but it is important theoretically.
Schlüsselwörter: Wachstum, theorie, methode, statistik, listing, basic, modell



Akamine, T. (1988). Evaluation of Error Caused by Histogram on Estimation of Parameters for a Mixture of Normal Distributions.
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.
Schlüsselwörter: Normalverteilung, basic, listing, methode, algorithmus, polyverteilung



Akamine, T. (1987). Comparison of Algorithms of Several Methods for Estimating Parameters of a Mixture of Normal Distributions (Vol. 37).
Schlüsselwörter: Normalverteilung, modell, lÄngenfrequenz, vergleich, methode, listing, basic, statistik, fischerei, algorithmus



Akamine, T. (1986). Expansion of growth curves using a periodic function and BASIC programs by Marquardt's method.
Zusammenfassung: The growth curves of von Bertalanffy, logistic and Gompertz models were expanded using a periodic function, f (t + 1) = f (t). Each model was expanded into l = l infinity (1exph sub(1)), l = l infinity /(1 + exph sub(1)) and l = l infinity exp(exph sub(1)) where h sub(1) = K(F(t)F(t sub(0))), F' = f, f = (1 + a)/2 + (1a)/2 multiplied by cos 2 pi (tt sub(1)) : a less than or equal to f less than or equal to 1. BASIC programs for each model were written by Marquardt's method. The following subjects were also considered : an expansion into another type, a parametererror analysis, a comparison with the original model and with Walford's graphical method, and a calculation to determine the extreme points of the growth rate. This expansion of the growth curves is useful and the programs are easily applied to other curves.
Schlüsselwörter: Wachstum, modell, methode, listing, basic, fischerei, statistik, algorithmus



Akamine, T. (1985). Consideration of the BASIC Programs to Analyse the Polymodal Frequency Distribution into Normal Distribution (Vol. 35).
Schlüsselwörter: Maximumlikeli, polyverteilung, normalverteilung, marquardt, statistik, basic, listing, theorie, algorithmus



Akamine, T. (1985). Consideration of the BASIC programs to analyse the polymodal frequency distribution into normal distributions.
Zusammenfassung: BASIC programs to analyse the polymodal frequency distribution into normal distributions were studied and a MaximumLikelihood program was compared with a LeastSquares program and its variations. The MaximumLikehood method is the most suitable procedure for the problem. The X super(2) minimum method is more suitable than the LeastSquares 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.
Schlüsselwörter: LÄngenfrequenz, methode, fischerei, basic, listing, statistik, mathematik, normalverteilung, modell, algorithmus

