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Autor  |
Akamine, T. |
| Titel |
An interval estimation for the Petersen method using Bayesian statistics |
Typ |
Zeitschrift, Artikel |
| Jahr |
1989 |
Publikation |
Bull. Japan Sea Reg. Fish. Res. Lab. Nissuiken Hokoku |
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Ausgabe |
39 |
Seiten |
19-35 |
| Schlüsselwörter |
Bayesian, binominal, basic, listing, methode, theorie, algorithmus |
| 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. |
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| Rufnummer |
218 |
Signatur |
2106 |
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| Autor |
Akamine, T. |
| Titel |
An interval estimation for extraction using Bayesian statistics |
Typ |
Zeitschrift, Artikel |
| Jahr |
1989 |
Publikation |
Bull. Japan Sea Reg. Fish. Res. Lab. Nissuiken Hokoku |
Kurztitel der Zeitschrift |
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Ausgabe |
39 |
Seiten |
9-17 |
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Bayesian, normalverteilung, binominal, statistik, theorie, algorithmus, listing, basic |
| 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 micro-computer than the conventional method. |
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| Rufnummer |
222 |
Signatur |
2110 |
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| Autor |
Akamine, T. |
| Titel |
Estimation of parameter for Richards model |
Typ |
Zeitschrift, Artikel |
| Jahr |
1988 |
Publikation |
Bull. Japan Sea Reg. Fish. Res. Lab. Nissuiken Hokoku |
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Ausgabe |
38 |
Seiten |
187-200 |
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Wachstum, theorie, methode, statistik, listing, basic, modell |
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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. |
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| Rufnummer |
206 |
Signatur |
2094 |
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| Autor |
Akamine, T. |
| Titel |
Evaluation of Error Caused by Histogram on Estimation of Parameters for a Mixture of Normal Distributions |
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Zeitschrift, Artikel |
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1988 |
Publikation |
Bull. Japan Sea Reg. Fish. Res. Lab. Nissuiken Hokoku |
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Ausgabe |
38 |
Seiten |
171-185 |
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Normalverteilung, basic, listing, methode, algorithmus, poly-verteilung |
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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. |
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219 |
Signatur |
2107 |
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| Autor |
Akamine, T. |
| Titel |
Expansion of growth curves using a periodic function and BASIC programs by Marquardt's method |
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Zeitschrift, Artikel |
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1986 |
Publikation |
Bull. Japan Sea Reg. Fish. Res. Lab. Nissuiken Hokoku |
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36 |
Seiten |
77-107 |
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Wachstum, modell, methode, listing, basic, fischerei, statistik, algorithmus |
| 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 (1-exph 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 + (1-a)/2 multiplied by cos 2 pi (t-t 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 parameter-error 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. |
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| Rufnummer |
207 |
Signatur |
2095 |
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| Autor |
Akamine, T. |
| Titel |
The BASIC program to analyse the polymodal frequency distribution into normal distributions with Marqualdt's method |
Typ |
Zeitschrift, Artikel |
| Jahr |
1984 |
Publikation |
Bull. Japan Sea Reg. Fish. Res. Lab. Nissuiken Hokoku |
Kurztitel der Zeitschrift |
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| Band |
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Ausgabe |
34 |
Seiten |
53-60 |
| Schlüsselwörter |
computer-programs, size-distribution, frequency-analysis, mathematical-models |
| Zusammenfassung |
The BASIC program for analysis of the polymodal frequency distribution into normal distributions is described. The algorithm of this program is Marqualdt's method. Gauss' elimination method is used to solve the simultaneous linear equations. Each parameter is scaled during calculation for faster convergence. User inputs the data and initial values of the parameters. It is adequate for convergence to set lambda = 10000 or larger. |
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63 |
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