Logarithmic Gauss distribution

Following these general statements on distribution functions, it is time to deal with functions which have special significance in the evaluation of data and for the determination of statistical characteristics from data. These functions will be norma distribution, logarithmic Gauss distribution, and Wei bull distribution. The form of the distribution and density function as well as the failure rate are shown in Table 4.3. 

Another important function in the data evaluation is the logarithmic Gauss distribution. It is characterized by the Jt > 0 area of application and is therefore well suited for data whose appearance above zero is set by natural givens (dimension, times, extent). According to the magnitude of parameters v and x, the failure rate increases or decreases. In the application of this function, the physical significance of the incident must be checked carefully. 

Table 4.3 Normal distribution, logarithmic Gauss distribution, and Weibuil distribution... 

It is realized experimentally that crystal size distributions are conveniently expressed as logarithmic Gauss functions ( ) ... 

According to [9,47] the integral curve of bubble distribution corresponds to natural logarithmic distribution (cutting the end parts of the curve). The natural logarithmic distribution is obtained when in the normal distribution function (Gauss s function)... 

Figure 7.1 Four steps of the Gauss-Newton algorithm showing convergence to matched-curvature normal distribution. The left-hand panels are the logarithm of the target and the quadratic that matches the first two derivatives at the value 0 i, and the right-hand panels are the corresponding target and normal approximation.

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