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These ML trees were inferred using 132 amino acid sites in the multiple alignment in Additional file 7 : Data S2, assuming JTT+Γ4 model (shape parameter α = 0.65).
The MtREV+G+F model (shape parameter = 1.198) [ 75- 77] was chosen for the Ste3A1 tree and the WAG+G+F (shape parameter = 1.0496) [ 76- 78] was selected for the Ste3A2 dataset.
To investigate the phylogenetic relationship between Bmp2/4/16 and P. marinus genes (Table 2), the maximum-likelihood (ML) tree was inferred using Tree-Puzzle [ 67], assuming JTT+I+Γ4 model (shape parameter of the gamma distribution α = 0.47).
This ML tree was inferred using 132 amino acid sites in the multiple alignment in Additional file 7 : Data S2, assuming JTT +Γ4+I model (shape parameter α = 0.58).
This ML tree was inferred using 130 amino acid sites in the multiple alignment in Additional file 7 : Data S2, assuming the JTT model with the proportion of invariable sites taken into account (JTT+Γ4+I model) (shape parameter α = 0.65).
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Afterward, to enhance the similarity of model related to the bearing faulty impulses, the model shape parameters are optimized using spectrum kurtosis and smoothing index.
The relationship between skewness, kurtosis and the Hermite model shape parameters is numerically inverted and an approximate solution is developed to improve the accuracy and simplify the application of the Hermite model to measured data.
The uncertain variables include the van Genuchten model shape parameters, the saturated and residual water contents, saturated hydraulic conductivity, dispersivity, dispersion coefficient, first-order decay terms, bulk density and partitioning coefficient.
If the Weibull model has shape parameter γ=1, then equation (1) becomes and this is the exponential model.
Compared to an experimental known, failure in Nobles Pond endscrapers is characterized by attrition, thus fits a Weibull model whose shape parameter β > 1.
For the Weibull model, the shape parameter is estimated as p=.537 (p value <0.01), which rejects that the separation hazard is constant and indicates that hazard is monotone decreasing (Cleves et al. 2008).
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