// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95
/*`
-This calculation is generalized as the free function called
-[link math_toolkit.dist.dist_ref.dist_algorithms find_location].
+This calculation is generalized as the free function called `find_location`,
+see __algorithms.
To use this we will need to
*/
For other applications, where it is more difficult or expensive to make many observations,
the confidence intervals are depressingly wide.
-See [link math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals Confidence Intervals on the standard deviation]
+See [link math_toolkit.stat_tut.weg.cs_eg.chi_sq_intervals Confidence Intervals on the standard deviation]
for a worked example
-[@../../../example/chi_square_std_dev_test.cpp chi_square_std_dev_test.cpp]
+[@../../example/chi_square_std_dev_test.cpp chi_square_std_dev_test.cpp]
of estimating these intervals.
/*`
Now we are getting really close, but to do the job properly,
we might need to use root finding method, for example the tools provided,
-and used elsewhere, in the Math Toolkit, see
-[link math_toolkit.toolkit.internals1.roots2 Root Finding Without Derivatives].
+and used elsewhere, in the Math Toolkit, see __root_finding_without_derivatives
But in this (normal) distribution case, we can and should be even smarter
and make a direct calculation.
Rearranging, we can directly calculate the required standard deviation:
*/
-normal N01; // standard normal distribution with meamn zero and unit standard deviation.
+normal N01; // standard normal distribution with mean zero and unit standard deviation.
p = 0.05;
double qp = quantile(N01, p);
double sd95 = (minimum_weight - mean) / qp;
// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957
/*`But notice that using '1 - over_fraction' - will lead to a
-[link why_complements loss of accuracy, especially if over_fraction was close to unity.]
+loss of accuracy, especially if over_fraction was close to unity. (See __why_complements).
In this (very common) case, we should instead use the __complements,
giving the most accurate result.
*/