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In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
In the case of a single factor the mixing model is easily stated. Each time period t there is a binary mixing variable b(t). If b(t)=0 then the factor return in that period is drawn from the normal distribution and if b(t)=1 it drawn from the jump distribution. Torre found that simultaneous jumps occur in factors.
Availability measures are classified by either the time interval of interest or the mechanisms for the system downtime. If the time interval of interest is the primary concern, we consider instantaneous, limiting, average, and limiting average availability.
The coverage probability, , for Neyman construction is the frequency of experiments in which the confidence interval contains the actual value of interest. Generally, the coverage probability is set to a 95 % {\displaystyle 95\%} confidence.
Failure rate is the frequency with which any system or component fails, expressed in failures per unit of time. It thus depends on the system conditions, time interval, and total number of systems under study. [1]
Hence, has been chosen accordingly in order to maintain the boundedness of the solution and the time interval of validity of the approximation is < <. The average theorem assumes existence of a connected and bounded region D ⊂ R n {\displaystyle D\subset \mathbb {R} ^{n}} which affects the time interval L {\displaystyle L} of the result validity.
The finiteness of the weakest-link chain model causes major deviations from the Weibull distribution. As the structure size, measured by N e q {\displaystyle N_{eq}} , increases, the grafting point of the Weibullian left part moves to the right until, at about N e q = 10 4 {\displaystyle N_{eq}=10^{4}} , the entire distribution becomes Weibullian.
In reflection seismology, the anelastic attenuation factor, often expressed as seismic quality factor or Q (which is inversely proportional to attenuation factor), quantifies the effects of anelastic attenuation on the seismic wavelet caused by fluid movement and grain boundary friction.