Evaluation of a Maximum-Likelihood Estimator for Analysis of Length-Frequency Distributions

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Abstract
The maximum‐likelihood estimation procedure described by Hasselblad is a statistical method applicable to estimates of population parameters in a mixture of normal distributions of component age‐groups. The method was used to estimate mean length‐at‐age and percentage composition of the component age‐groups in 10 collections of largemouth bass (Micropterus salmoides) for which age was determined by the scale method. Compared to fish aged by the scale method, the error of the estimates of mean length‐at‐age averaged 3.2%. About one‐third of the 31 frequency distributions, and six of seven distributions with more than 100 fish, deviated significantly from that of a normal distribution; many distributions exhibited skewness and kurtosis. However, the general failure of the samples to fit characteristics of the normal curve did not greatly influence accuracy in estimating mean length. The average error of the estimates of percentage composition by age was 28%; the magnitude of this error was related to the degree of asymmetry and a large standard deviation of length. The latter was apparently related to a prolonged and disjunct spawning season which produced multimodal distributions within each age‐group.

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