HCL Sample Clauses

HCL. The fit of truncated normals and skew normals as approxima- tions to the distribution of non-differentially expressed proteins, f0, having support [ 1.143, 1.143]. A visual comparison of the ECDF to the CDF again indicate: the lack-of-fit of single component models and the excellent fit of the skew normal mix- ture. f0 pˆ0 pˆ Parameter Estimates p ∗ Nt (µ1, σ1) + (1 − p) ∗ Nt (µ2, σ2) 0.871 0.139 µˆ1 = 0.498 σˆ1 = 2.021 µˆ2 σˆ2 = −0.135 = 0.228 p ∗ SNt (µ1, σ1, λ1) + (1 − p) ∗ SNt (µ2, σ2, λ2) 0.921 0.892 µˆ1 = 0.153 σˆ1 = 0.534 λˆ1 = −1.765 µˆ2 σˆ2 λˆ2 = −0.105 = 0.613 = −0.081 Table 3.1: Sample A : Parameter estimates under each of the fitted mixture models for f0. pˆ0 is the estimated proportion of non-differentially expressed proteins under each model. f0 pˆ0 pˆ Parameter Estimates p ∗ Nt (µ1, σ1) + (1 − p) ∗ Nt (µ2, σ2) 0.899 0.117 µˆ1 = 0.311 σˆ1 = 1.821 µˆ2 σˆ2 = −0.128 = 0.428 p ∗ SNt (µ1, σ1, λ1) + (1 − p) ∗ SNt (µ2, σ2, λ2) 0.951 0.829 µˆ1 = 0.079 σˆ1 = 0.301 λˆ1 = −1.961 µˆ2 σˆ2 λˆ2 = −0.705 = 2.858 = 6.868 Table 3.2: Sample B : Parameter estimates under each of the fitted mixture models for f0. f0 pˆ0 pˆ Parameter Estimates p ∗ Nt (µ1, σ1) + (1 − p) ∗ Nt (µ2, σ2) 0.921 0.335 µˆ1 σˆ1 = −0.120 = 1.775 µˆ2 = 0.061 σˆ2 = 0.639 p ∗ SNt (µ1, σ1, λ1) + (1 − p) ∗ SNt (µ2, σ2, λ2) 0.960 0.382 µˆ1 σˆ1 λˆ1 = 0.018 = 1.751 = −0.064 µˆ2 = −0.256 σˆ2 = 0.550 λˆ2 = 0.947 Table 3.3: Hela Cell Line : Parameter estimates under each of the fitted mixture models for f0.
Sample 1
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HCL. The results of fitting the same four distributions to the f distribution of the HCL data is shown in Figure 3.5. The estimated parameters for each model setup is given in Table 3.5. Here again the two component Student’s t mixture fails to capture the middle part of the density histogram of the z values. The two component normal mixture estimates the central region and the left tail reasonably well, but the density estimate drops to zero two quickly at the right tail. The skew-t mixture and the generalized hyperbolic both approximate the data quite well. However, compared to the skew-t mixture, the fit of the generalized hyperbolic is smoother. This is because the generalized hyperbolic, since it is a single component model, does not follow the peaks of the histogram too closely.
Sample 1
HCL. (a) HCL is and shall be a private company limited by shares incorporated under the Companies Ordinance.
Sample 1

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