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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, poly-verteilung
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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
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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 (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.
Schlüsselwörter: Wachstum, modell, methode, listing, basic, fischerei, statistik, algorithmus
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Akamine, T. (1985). Consideration of the BASIC Programs to Analyse the Polymodal Frequency Distribution into Normal Distribution (Vol. 35).
Schlüsselwörter: Maximum-likeli, poly-verteilung, normalverteilung, marquardt, statistik, basic, listing, theorie, algorithmus
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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 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.
Schlüsselwörter: LÄngenfrequenz, methode, fischerei, basic, listing, statistik, mathematik, normalverteilung, modell, algorithmus
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Akamine, T. (1984). The BASIC program to analyse the polymodal frequency distribution into normal distributions with Marqualdt's method.
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.
Schlüsselwörter: computer-programs, size-distribution, frequency-analysis, mathematical-models
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Albrecht, H. (1991). Microsofts Fünfte.
Schlüsselwörter: Software, test
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Albrecht, H. (1983). Die Prostastacidae n. fam., fossile Vorfahren der Flusskrebse? (Vol. 1983).
Schlüsselwörter: Krebs, Prähistorisch, Systematik
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Albrecht, H. (1983). Besiedlungsdichte und ursprünglich holozäne Verbreitung der europäischen Flußkrebse (Decapoda: Astacidae) (Vol. 6).
Schlüsselwörter: Krebs, Verbreitung, Vorkommen, Geographisch
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Albrecht, H. (1982). Das System der europäischen Flusskrebse (Decapoda, Astacidae): Vorschlag und Begründung (Vol. 79).
Schlüsselwörter: Krebs, Systematik, Flusskrebs
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