Arithmetic-average combination

A particular situation where bias may be important is in statistical meta-analysis, where statistical estimates are combined across studies. When estimates from individual studies may be averaged arithmetically, it is better to average unbiased estimates (Rao 1973, Section 3a). In case of biases that are consistent across studies, an arithmetic average would have a bias of the same sign, regardless of the number of studies included in the analysis. The average of biased estimates could fail to be consistent (in the statistical sense). 

Note that the operative temperature will be the arithmetic average of the ambient and surrounding surface temperatures when the convection and radiation heat transfer coefficients are equal to each other. Another environmental index used in thermal comfort analysis is the effective temperature, which combines the effects of temperature and humidity. Two environments with the same effective temperature evokes the same thermal response in people even though they are at different temperatures and humidities. 

If I for tensile strength is greater than zero, the components of the blends are normally considered to be compatible, which is a visually homogenous mixture with enhanced physical properties over the constituent polymer. Otherwise, the blend is usually an incompatible system when I for tensile strength is less than zero. If I equals zero, the properties of the combination are equal to the weighted arithmetic average of the constituent properties as shown below ... 

B. Geometrical configuration is considered as a very small cube with linear changes of the variables considered along its sides. Consideration of very small cube size in the derivations implies the assumptions of homogeneity, uniformity and isotropy automatically. Such a combination of assumptions further implies the use of the arithmetic average and linearity concepts. 

The usefulness of the concept of expectation, as defined above, is that it corresponds to our intuitive idea of average, or equivalently to the center of gravity of the probability density distribution along the x-axis. It is easy to show that combining Eqs. (7.15) and (7.6) yields the arithmetic average of the random variable for the entire population ... 

When the point values are average probabilities, the overall result from combining system.s as combinations of sequences and redundancies is found by simply combining the mean probabiliiies according to the arithmetic operations. 

The empirical AN and DN indexes obtained by our approach also lend themselves easily for calculations of pair interaction numbers. Tliere is no formal theoretical guideline on how best to combine individual AN and DN numbers. Arithmetic, geometric and harmonic mean averaging may be used, with a decision as to preferred approach left to an empirical examination of results. One pair interaction number, I p, which has proven to be useful, is defined as follows ... 

It is fonnd from Figure 16.3 that, the dielectric constants of the composites are non-linearly dependent on volume % of BNN. This shows that the constituent capacitors formed by dielectrics fillers and polymer in the composites are not in parallel combination. From Figure 16.3, it is clear that the inverse of dielectric constant cnrve is not in a harmonic pattern, constituent capacitors formed by dielectrics fillers and polymer in the composites is not in series combinatiom One can choose to model composites as having capacitance in parallel (upper bound) or in series (lower bound). In practice, the answer will lie somewhere between the two. Physically, in composites with (0-3) structures which generally conform to special logarithmic equation, the relation assumes the form of Lichteneker and Rother s (Lich-teneker, 1956) more appropriate to composite stractures where the two-component dielectrics are neither parallel nor perpendicular to the electric field that is, the vahd averages are neither arithmetic nor harmonic. 

---