Location parameters

Gn L) is often difficult to determine for a given load distribution, but when is large, an approximation is given by the Maximum Extreme Value Type I distribution of the maximum extremes with a scale parameter, 0, and location parameter, v. When the initial loading stress distribution,/(L), is modelled by a Normal, Lognormal, 2-par-ameter Weibull or 3-parameter Weibull distribution, the extremal model parameters can be determined by the equations in Table 4.11. These equations include terms for the number of load applications, n. The extremal model for the loading stress can then be used in the SSI analysis to determine the reliability. 

A location parameter is the abscissa of a location point and may be a measure of central tendency, such as a mean. 

A scale parameter determines the location of fractiles of the distribution relative to some specified point, often the value of the location parameter. 

As with the Langmuir adsorption isotherm, which in shape closely resembles Michaelis-Menten type biochemical kinetics, the two notable features of such reactions are the location parameter of the curve along the concentration axis (the value of Km or the magnitude of the coupling efficiency factor) and the maximal rate of the reaction (Vmax). In generic terms, Michaelis-Menten reactions can be written in the form... 

It can be seen from Equation 2.2 that for positive non-zero values of p2, ptotai < pi- Therefore, the location parameter of the rectangular hyperbola of the composite set of reactions in series is shifted to the left (increased... 

The term p is the coupling efficiency constant for the second function. The location parameter (potency) of the second function (denoted K0bS) is given by... 

FIGURE 3.2 General curve for an input/output function of the rectangular hyperbolic form (y = 50x/( 1 Ox + 100)). The maximal asymptote is given by A/B and the location parameter (along the x axis) is given by C/B (see text). 

The form of that function is shown in Figure 3.2. There are two specific parameters that can be immediately observed from this function. The first is that the maximal asymptote of the function is given solely by the magnitude of A/B. The second is that the location parameter of the function (where it lies along the input axis) is given by C/B. It can be seen that when [Input] equals C/B the output necessarily will be 0.5. Therefore, whatever the function the midpoint of the curve will lie on a point at Input = C/B. These ideas are useful since they describe two essential behaviors of any dmg-receptor model namely, the maximal response (A/B) and the potency (concentration of input required for effect C/B). Many of the complex equations... 

Equation 6.19 predicts an increasing IC50 with either increases in L or 1. In systems with low-efficacy inverse agonists or in systems with low levels of constitutive activity, the observed location parameter is still a close estimate of the KB (equilibrium dissociation constant of the ligand-receptor complex, a molecular quantity that transcends test system type). In general, the observed potency of inverse agonists only defines the lower limit of affinity. 

Alter the location parameter of the concentration-response curve... 

The middle of the concentration range should be as near to the location parameter (i.e., EC50, IC50) of the curve as possible. 

Fig. 1). If an agonist produces a submaximal system response it is called a partial agonist (Fig. 1). While the potency of an agonist is quantified by the location parameter of the dose-response curve (EC50), a reflection of (but not a direct measure of) the intrinsic efficacy of an agonist is given by its maximal response. 

Drug-Receptor Interaction. Figure 2 Relationships between affinity and efficacy with different agonist response patterns, (a) For partial agonists, differences in maximal responses between agonists relate to differences in efficacy. Differences in the location parameter of the concentration-response curve (potency) indicate differences in affinity, (b) For full agonists, differences in potency indicate differences in either affinity, efficacy or both. 

The maximum search function is designed to locate intensity maxima within a limited area of x apace. Such information is important in order to ensure that the specimen is correctly aligned. The user must supply an initial estimate of the peak location and the boundary of the region of interest. Points surrounding this estimate are sampled in a systematic pattern to form a new estimate of the peak position. Several iterations are performed until the statistical uncertainties in the peak location parameters, as determined by a linearized least squares fit to the intensity data, are within bounds that are consistent with their estimated errors. 

Huber, R J. (1964). A robust estimation of a location parameter. Ann. Math. Stat. 35,73-101. 

For a three-parameter distribution, t is replaced by t-t where t is called the location parameter. If failures are numbered in successive order and expressed as a fraction (n) of the total number, a plot of log (-In [1- p]) against log (t) should yield a straight line of slope P with the point t = tc corresponding to n = 0.632 (0.632 = 1-1/c, where e is the base of the natural logarithms). 

Davies, L., Asymptotic behavior of S-estimators of multivariate location parameters and dispersion matrices, Ann. Stat., 15, 1269-1292, 1987. 

Radial basis function networks with more than one input unit have more parameters for each hidden node e.g.,. if there are two input units, then the basis function for each hidden unit j needs two location parameters, pij and p2j, for the center, and, optionally, two parameters, Oij and a2j, for variability. The dimension of the centers for each of the hidden units matches the dimension of the input vector. 

Two classes of parameters are needed in models of observations location parameters 6i to describe expected response values and scale parameters dg to describe distributions of errors. Jeffreys treated 6i and dg separately in deriving his noninformative prior this was reasonable since the two types of parameters are unrelated a priori. Our development here will parallel that given by Box and Tiao (1973, 1992), which provides a fuller discussion. The key result of this section is Eq. (5.5-8). 

Any model linear in its location parameters 0 has a uniform Jeffreys prior p 6i) over the permitted range of 0 . This condition occurred in Examples 5.6 and 5.8, where the model = p + eu with location parameter p was used. The Jeffreys prior p(0 ) is likewise uniform for any model nonlinear in 0 , over the useful range of its linearized Taylor expansion that we provide in Chapters 6 and 7. 

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