PubMed · 7694252
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M Malik. 1993. Random numbers.. https://doi.org/10.1111/j.1540-8159.1993.tb00999.x
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Eleven numerical methods for estimation of AUC (including 4 new methods) and 22 methods for AUMC (including 8 new methods) were tested on large simulated noisy datasets representing bolus, oral and infusion concentration-time profiles. Some methods were unacceptable because their mean error was large; these included a commonly recommended form of the linear trapezoidal rule for AUMC. Others, notably Lagrange and cubic spline methods, were unacceptable because the variance of their estimates was large. These methods should be abandoned. A simple and easily programmed new method, parabolas-through-the-origin then log-trapezoidal rule, performed especially well.
The data from an integrated numerical classification was used to construct identification schemes for some fasciculate penicillia. The identification schemes were presented as a synoptic key and a frequency matrix for computer-assisted identification. Statistical testing of the frequency matrix showed that although character separation values were generally low, only four pairs of taxa showed overlap greater than that expected for a rectangular distribution. The identification schemes were tested practically with 52 previously studied strains and 51 further cultures. A synoptic key based on 10 and 90% cutoff limits was used to correctly identify 44 of the 51 additional strains, although this proved very sensitive to single test discrepancies. The frequency matrix was used to correctly identify 45 of the additional strains with a Willcox probability score and this was compared to identifications based on the modal likelihood fraction.