Running averages

Tlie expected value of a random variable is the average value of the random variable. The expected value of a random variable X is denoted by E(X). The expected value of a random variable can be interpreted as the long-run average of observations on tlie random variable. The procedure for calculating the expected value of a random variable depends on whether the random variable is discrete or continuous. 

Ten-year running average summertime monthly maximum and minimum temperatures in Los Angeles, California (1877-1997). The average is calculated as the average temperature of the previous four years, the current year, and the next five years. Note that the maximum temperatures have increased about 2.5 C (4.5T) since 1920. 

Assume that we bin the interval of interest for and that we have collected nk (N ) samples in bin k after N steps in a molecular dynamics simulation. We use those samples to compute a running average of the force acting along ... 

Fig. 6.12. Block averaging of an FEB or NEW calculation can be used to create a smoothed running profile. This contrasts with the jagged steps of a running average based on the same data. The running steps occur with the relatively rare sampling of events in the tails of the distribution that dominate the relative free energy estimate. The smoothed running curve uses the block procedure described in the text...

Key Marburg, Germany oak ------, 5 samples ( 30 years) running average , 4-7 year samples ... 

Seasonal and interannual trends in atmospheric carbon dioxide concentrations reported as mole fraction in dry air. (a) Monthly mean values at Mauna Loa Observatory, Hawaii. Data are also presented as 6-month running average to eliminate the seasonal effects and (b) three-dimensional representation of latitudinal distributions of monthly mean values. Source After P. Tans and T. Conway, NOAA/ESRL Global Monitoring Division (www.esrl.noaa.gov/gmd/ccgg/trends). (See companion website for color version.)... 

AVG(x) running average of x over the range of the x-axis variable ... 

Fig. 6.30. Results of computer simulations for the time-development of critical exponent a (average for each time decade) observed in the reaction A + B — 0, d = 1 and nA(0) = riB(O) = 0.4. Lattice contains 105 sites, results are for cyclic boundary conditions and 10 runs averaged. Full lines are for the excluded volume case, whereas in dashed line any number of particles could occupy a given site.

Emissions Parameter Permit Section Module V" Permit Limit MPF Results (four-run average) Compliance Limit Met... 

The magnitude and phase of the incoming signal are computed on a block-by-block basis using the FFT. The noise magnitude spectrum is calculated as a running average... 

The differences between 100 and 400 vials per run average Tjce for 100 vials is always lower than that for 400 vials. The amount of water vapor transported per unit time with 100 vials is smaller than with 400 vials, which requires a lower vapor pressure as shown by Tice The influence of the number of vials on Tice, i.e. the pressure necessary to transport the vapor is small provided that s is small compared with max. s (see Figure 1.89). This has two effects (1) if Tice has to be, e.g., below -29 °C, 100 vials can be dried with the process data used, but with 400 vials... 

It is customary to collect data from several runs, averaging the counts over those runs. The number of iterations performed depends on the system under study. The data collection may be over several iterations following the achievement of a stable or equilibrium condition. This stability is reckoned as a series of values that exhibit a relatively constant average value over a number of iterations. In other words, there is no trend observed toward a higher or lower average value. 

Asphaltenes + Polar Aromatics Number of Runs Average Coke... 

---