Moment properties of estimators for an exponential regression with type 1 censoring

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Improved estimators for the shape parameter in gamma regression

A regression model is considered in which the response variables have gamma distributions with a common shape parameter. A review is given of existing estimators for the shape parameter. Bias expressions for the maximum likelihood estimates of the regression coe f f i c i ent s and the shape parameter are developed. A new estima t o r f o r t h e shape parameter based on bias correction for the maximum likelihood estimator is shown to have markedly better variance and mean square error properties in small to moderate sized samples. Approximations to the low order moments of the Pearson statistic are derived for gamma regression models with general link functions. These are used for the case of a logarithmic link to develop new estimators for the shape parameter which have better moment properties than the estimators based on the Pearson statistic which have been used previously. Finally, the small sample variance and mean square error efficiencies of the estimators relative to the maximum likelihood estimator are evaluated by simulation for the case of a single explanatory variable and a logarithmic link, for a range of sample sizes less than or equal to 100

Kinetic characterisation of the FAD dependent monooxygenase TropB and investigation of its biotransformation potential

\ua9 2015 The Royal Society of Chemistry. Achieving regio-specific hydroxylation of aromatic compounds remains a major challenge in synthetic chemistry. By contrast, this transformation is readily accomplished in nature through the action of FAD-dependant monooxygenase enzymes. Here, we report the kinetic characterisation of one such enzyme, TropB, from the stipitatic acid biosynthetic pathway. Analogues of the TropB natural substrate, 3-methyl-orcinaldehyde, were synthesised and used to examine the substrate selectivity of this enzyme. TropB displays broad substrate tolerance, for instance accepting single-ring aromatic substrates containing a range of C-1 substituents with varying electronic and steric properties. These include nitro, nitrosyl, alkyl, and aryl keto groups. Bicyclic substrates, however, were rejected by TropB. Additionally, C-5 substituents on single-ring aromatic substrates were not tolerated whereas the presence of a 6-methyl group was found to be important for substrate binding. Docking studies were employed to investigate and understand the broad substrate selectivity of TropB and identifies the key structural elements of its substrates. Our work has shown that TropB is an attractive target for biocatalyst engineering and industrial aromatic hydroxylation