Normal probability function

In the method of the software package ALLOC of Hermans and Habbema the individual potential function has the form of a multidimensional normal probability function, and the overall function gives the conditional probability density of each category, so that the basic concepts of BA can be applied. 

The normal probability function as expressed by Eq. (14) is useful in theoretical treatments of random errors. For example, the normal probability distribution function is used to establish the probability Hthat an error is less than a certain magnitude 8, or conversely to establish the limiting width of the range, —8 to 8, within which the integrated probability P, given by... 

Of special interest is the normal probability function discussed in Chapter II [see Eq. (11-14)] ... 

The normal probability function table given in the appendix d this book can also be used for values of the log-normal distribution function, f, and the log-normal cumulative distribution function, F. In these tables Z = [ln(d/cy/(In o- )] is used. A plot of the cumulative log-normal distribution is linear on log-normal probability paper, like that shown in Figure 2.11. A size distribution that fits the log-normal distribution equation can be represented by two numbers, the geometric mean size, dg, and the geometric standard deviation,. The geometric mean size is the size at 50% of the distribution, d. The geometric standard deviation is easily obtained finm the following ratios ... 

Model Distribution While a PSD with n intervals is represented by 2n + 1 numbers, further data reduction can be performed by fitting the size distribution to a specific mathematical model. The logarithmic normal distribution or the logarithmic normal probability function is one common model distribution used for the distribution density, and it is given by... 

However, the majority of real systems cannot be quantified according to an unique elementary process. Generally, TSDC results are interpreted formally in terms of a distribution of parallel (uncoupled) activated Debye-like processes. Therefore, considering, as discussed in the first section, a distribution of activation times with a normalized probability function p(ln x), the polarization is given by ... 

Relationship with Normal Probability Function f t) /(f)df = ierf... 

NORMAL PROBABILITY FUNCTION Table of the normal distribution... 

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