Sentence examples for fractional distribution from inspiring English sources

Different superficial velocities of fluidizing gas are defined to investigate the hydrodynamics of the fluidized beds and the consequent influence on the yield fractional distribution of end-products.

While in our previous paper, we showed that a fractional distribution cannot generally be defined as a conventional distribution.

As the hardness of natural waters is mainly conditioned by the existence of Ca2+ and Mg2+ ions, it was interesting to separately observe the fractional distribution of these salts by the aforementioned method.

A numerical development of implied fractional distribution to a constant hazard rate (as it is the case for an exponential default distribution) and its CDF are given in Figs. 1 and 2 for fractional parameters H=0.5, 0.6, and 0.75.

The implied hazard fractional probability density f H (t) as well as its cumulative fractional distribution, define uniquely their fractional hazard rate implied distribution: left{ begin{array}{ll} f_{H}(t)=h_{H}(t)expleft -int_{0}^{t} h_{H}(tau)dtauright), 1-F_{H}(t)=expleft -int_{0}^{t} h_{H} tau dtauright). end{array} right.

Unlike the definition of a fractional probability distribution based on Liouville's and Caputo's fractional operators that generally define "incomplete" distributions (see Tapiero and Vallois (2016) on fractional randomness), a fractional distribution implied by its fractional hazard rate provides a complete distribution.

Note that initially, for a non-fractional distribution f(0)=α=0.10, while for fractional distributions (with H<1), f H (0)<α, as this was case for an exponential distribution.

The purpose of this paper consists of defining fractional hazard rates implied fractional distributions and to highlight their usefulness to granular default risk distributions.

In this paper we suggest a fractional hazard rate to define conventional fractional distributions and suggest that the fractional hazard rate is a reasonable and consistent approach to define fractional default distributions and therefore useful in the definition of risk models that define the increased (or decreased) risks that occur due to model granularity.

However, the fractional distributions of different apoE were very different.

We found striking similarities in the fractional distributions between different populations of CD and UC patients included in the entirety of our study.