Distribution continuous -, discrete

Many companies choose to represent a continuous distribution with discrete values using the p90, p50, plO values. The discrete probabilities which are then attached to these values are then 25%, 50%, 25%, for a normal distribution. 

Dispersed bubble (DB) - The gas phase is distributed as discrete bubbles within a continuous liquid phase. At the transition boundary most bubbles are located near the top. As the liquid rate increases, the bubbles are more uniformly dispersed. 

Moments 92. Common Probability Distributions for Continuous Random Variables 94. Probability Distributions for Discrete Random Variables. Univariate Analysis 102. Confidence Intervals 103. Correlation 105. Regression 106. 

Bubbly flow. Here the bubbles were shorter than the tube diameter and the vapor phase was distributed as discrete bubbles in a continuous liquid phase (Fig. 2.30a). 

Consider a solid feed consisting of a mixture of different-size particles. The size distribution of this feed can be represented either as a continuous distribution or as a discrete distribution. We use the latter representation because screen analysis, our way of measuring size distributions, gives discrete measurements. 

The cdf of the empirical distribution converges in probability to the true cdf, as n increases. However, in small samples the empirical distribution may have some features that we do not want to extrapolate to the population. The empirical distribution is discrete (with positive probability only for observed values), whereas the population distribution may be conceived as continuous. With n too small there may actu-... 

Figure 14.3. Particle size distribution, (a) Discrete and continuous cumulative particle size distribution, (b) Discrete and continuous particle size distribution, (c) Volume distribution plotted in accordance with equation 3. (d) Particle size distributions at four depths in a calcareous sediment from west equatorial Pacific Ocean, 1°6.0 S, 161 36.6 E, box core No. 136, water depth 3848 m. (From Lerman, 1979.)...

One reason the normal distribution is so important is that a number of natural phenomena are normally distributed or closely approximate it. In fact, many experiments, when repeated a large number of times, will approach the normal distribution curve. In its pure form, the normal curve is a continuous, symmetrical, smooth curve shaped like the one shown in Figure 134. Naturally, a finite distribution of discrete data can only approximate this curve. 

Mononucleation Mononucleation events at electrochemical interfaces have been observed in potential step experiments by monitoring current, charge, or capacitance as a function of time under conditions of (1) low supersaturation and (2) small, defect-free electrode surfaces. These experiments offer the unique opportunity to determine simultaneously absolute rates of the nucleation and growth processes. The formation of the critical nucleus appears stochastically in time and space (Fig. 3). The time distribution (continuous) of the birth events of critical nuclei (discrete), as indicated by the onset of the subsequent growth transient (current/charge increase, decrease of interfacial capacitance), within a sufficient long train of repetitive transient experiments under identical conditions, leads... 

During a sabbatical in 1999, he developed a new and original continuous-discrete simulation software. This was done in collaboration with a commercial software distributor. The developed modules are now part of the basic version of a software that is distributed worldwide. 

Comparisons of continuous distributions to discrete experimental data must accommodate the size ranges or bins selected by the investigators for the bubble count. The measured probability of bubbles at a given size, V, is actually the fraction of those measured that falls in a range, say v, to Vj. 

The center of an experimental arc is frequently displaced below the real axis because of the presence of distributed elements in the material-electrode system. Similar displacements may also be observed in any of the other complex planes plots (Y, M, or e). The relaxation time T is then not singlevalued but is distributed continuously or discretely around a mean, = 0)m. The angle 8 by which such a semicircular arc is depressed below the real axis is related to the width of the relaxation time distribution and as such is an important parameter. 

Pig. 6. Distribution of discrete measurement sites of resolution LxL over a continuous gradient library. Measurement sites have average T and (p with gradient variance AT and A. ... 

Whereas in small particles the electrons are distributed over discrete energy levels, at a metal surface this electron distribution becomes continuous. Bonding between small particles and adsorbing molecules can be discussed in terms of the formation of bonding and antibonding orbitals. 

Controllers are devices that are meant to keep a specific controlled variable constant despite outside disturbances. One differentiates between continuous, digital, and On-Off controllers, depending on whether the output is continuous, discrete, or on-off. The great majority of controllers have been continuous, but the digital controller is now commonplace due to the widespread use of computers and distributed control systems. 

In Equation 2-10, we introduced continuous line source distributions, that is, taking p(x,y) = j f(Q log V (x- )2 + y d + H over the integration limits (-l,-i-l), and later obtained closed form solutions. Suppose that we instead model fractures using distributions of discrete point sources, that is,... 

Probability distributions may be continuous or discrete. In continuous distributions, the variable may take all values in an interval and may be represented by a smooth curve. The distribution shown in Figure 7.3 is a continuous distribution. In discrete distributions, the variable takes on nonnegative inte-... 

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