Density cumulative

This expression gives the cumulative density of absorbing states between energies 0 and E (note the change of sign in front of e). This expression can be used to estimate the total excited state absorption by computing... 

Figure 4. Cumulative densities of states for hypothetical model of Ar, used by Berry et al. for solidlike and liquidlike limiting cases.

Cumulative density of fracture trace length d(L) is given by (Nirex, 1997a)... 

Now suppose that a group of patients is included in a clinical trial because they have measured values in excess of some threshold k. We then have X > k. X now has a truncated Normal distribution. Let cJ)(m) be the probability density function of a standard Normal distribution and 0(m) be the distribution function (cumulative density function). Let a= k — iE)jcT- andZ = (X - then P(X>k) = P(Z >a) = l — 4>(a). 

Example 2.23 Cumulative Density Function of Normal Distribution. Suppose that the breaking strength (in pounds) of a rope has an W(205, 5 ) distribution. A rope is considered defective if the breaking strength is less than 200 pounds. What proportions of ropes are... 

In addition to PDFs we sometimes use cumulative density functions (CDFs). These are defined as... 

Figure 4 shows the cumulative density function (CDF) of the pore size distribution of sample A (1 x 1 x 9.6 mm ). Similar curves were obtained for the other samples investigated, but are not shown here. 

Figures 18 and 19 show respectively the output pdf fy(y) itself and the cumulative density function (cdf) of the considered example.

The variance of the distribution at different time horizons seems to be constant which can also be seen out of Fig. 7 considering the 3 nearly parallel cumulated density functions. 

Consider a standard newsvendor with a procurement cost c and sell to his customers at a fixed unit price r. The customer demand D follows a probability density function (PDF)y(-) and a cumulative density function (CDF)F(-). The newsvendor has only one order opportunity and determines his order quantity before the actual demand is realized. If the newsvendor underorders, he will suffer lost sales. For simplicity, we assume zero shortage cost throughout the chapter. If he over-orders, he will dispose the unsold inventory at salvage price v, which leads to a loss as well. Moreover, the newsvendor has a preset target profit of t, and his objective is to choose an order quantity g to maximize the probability of achieving the target to maximize P (q) = P U(q)>t. ... 

Here subscript cum in Nann means that this EUE index is produced by the so-called cumulant density matrix (6.45), as such RDM constmctions are termed in the current RDM theory [51]. For practical computations, within FCI or RAS-CI (restricted active space Cl), more suitable is a spin-free expression from [35]. 

Complementary cumulative density function (CCDF), i.e., density of the remaining pad material at a given height z at time t, is given as... 

In equation 5, ( ) is the standard normal cumulative density function. The schematic representation of the FORM method is shown in Figure 1.1. 

Of interest here is the cumulative density of states N E) and the local density of states p E), formally defined by the exact expressions ... 

We recall that the classical approximation to the cumulative density of vibrational states can be written as ... 

Figure 6.1 Cumulative density of states for a system of three coupled harmonic oscillators. The Hamiltonian is given by Equation (6.15) with (o —, oj = 4, (Mj = 5, c5i = 0.1, and di = O.IL The red line is the exact adiabatic state count using the levels given by Equation (6.19). The dotted green line is result of the semiclassical adiabatic method. Equation (6.12). The blue line is the traditional uncoupled harmonic description based on the potential minimum.

Assuming the transition state is associated with the ridgeline at 5 = 5q, we have the vibrational cumulative density of states computed by the semiclassical prescription ... 

---