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  • for 68 % coverage, b = 1;
  • for 95 % coverage, (symbol to be inserted) = 1.96;
  • for 95.5 % coverage,  (symbol to be inserted)= 2;
  • for 99 % coverage, (symbol to be inserted) = 2.58;
  • for 99.9 % coverage, (symbol to be inserted) =3.29.

    The exact values can be easily determined by using the inverse Gaussian function.

(EQ to be inserted) 

Mathinline
body$v({{R}_{\max }})={{P}_{VLT}}+{{g}_{VLT}}+{{g}_{VLR}}-sen{{s}_{VLR}}-{{F}_{median}}({{f}_{VLR}},{{h}_{VLR}},{{h}_{VLT}},{{R}_{\max }},env)-b\sigma $
                     (Eq. 174)

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The determination of the zero of function v, is made through a recursive method such as regula-falsi used in logarithmic scale which should yield a better precision. The solution of such a method provides the following equation:

            (EQ to be inserted)                       

Mathinline
body${{\tilde{R}}_{\max }}={{R}_{\max 0}}-\frac{{{R}_{\max 0}}-{{R}_{\max 1}}}{v({{R}_{\max 0}})-v({{R}_{\max 1}})}v({{R}_{\max 0}})$
                        (Eq. 175)


In this case, formulas given for  need to be inverted. 

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In this case, formulas given for (EQ to be inserted - only half is copied with math tool)  need to be inverted.


Note 1: The inverse of the normalised Gaussian cumulative distribution is implemented through a piece approximation.

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