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In time series analysis and statistics, the cross-correlation of a pair of random process is the correlation between values of the processes at different times, as a function of the two times. Let ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} be a pair of random processes, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be ...
The characteristic aspect of the machine's design is its automatic performance of elapsed-time calculations, as calculating the difference between two times manually is a tedious and error-prone process, and the machines quickly gained popularity. Abbott founded the Calculagraph Company in New York City, and later moved to New Jersey. The ...
The samples included in the average can be an arbitrary subset of all the samples in the signal (e.g., samples within a finite time window or a sub-sampling of one of the signals). For a large number of samples, the average converges to the true covariance. Cross-covariance may also refer to a "deterministic" cross-covariance between two signals.
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
Mean time between failures (MTBF) describes the expected time between two failures for a repairable system. For example, three identical systems starting to function properly at time 0 are working until all of them fail. The first system fails after 100 hours, the second after 120 hours and the third after 130 hours.
Fold change is a measure describing how much a quantity changes between an original and a subsequent measurement. It is defined as the ratio between the two quantities; for quantities A and B the fold change of B with respect to A is B/A. In other words, a change from 30 to 60 is defined as a fold-change of 2.
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A.
The equation of time describes the discrepancy between two kinds of solar time. The two times that differ are the apparent solar time , which directly tracks the diurnal motion of the Sun , and mean solar time , which tracks a theoretical mean Sun with uniform motion along the celestial equator .
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