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Bad initial approximation for an invIncompleteBeta #13
For small fraction of values initial approximation is so bad that answer couldn't be calculated at all
Initial approximation for x indeed falls out of [0,1] range and so inverse couldn't be calculated. Currently initial guess from AS64,AS109 is used. Guess from numerical recipes is free from this problem but have poor precision. Current guess require 2 iterations on average and one from recipes frequently require more than 10.
Probably we should take algorithm for initial guess from boost: http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html (futher references on the page)