
Boost Users : 
Subject: Re: [Boostusers] Newbie math question  roots of a distribution
From: Benjamin Ward (ENV) (B.Ward_at_[hidden])
Date: 20140207 09:48:02
Hi,
I'm not sure this is right, since the inverse cdf: returns a value x such that cdf(dist(N,p), x) == P.
I'm trying to find 'p'. And if I understand it correctly the examples of the inverse cdf still have to specify p first.
Best,
Ben.
________________________________________
From: Boostusers [boostusersbounces_at_[hidden]] on behalf of John Maddock [boost.regex_at_[hidden]]
Sent: 07 February 2014 10:07
To: boostusers_at_[hidden]
Subject: Re: [Boostusers] Newbie math question  roots of a distribution
> But now I'd like to find the root of the cdf, in other words, I want to find the value of successprob, from numbertrials and numbersuccesses and ans.
>
> Let's define ans as 0.95, by finding the root of cdf(mydistribution, numbersuccesses)  1, using a root finding algorithm, I should be able to get the value of successprob. I've tried reading the roots documentation and looking at some examples but they use simple functions like x * sin(x)  there is only one variable and it is x, the binomial cdf has quite a few variables  number of trials, number of successes, probability of a single success. How can I define a function with boost::math::binomial that could be used with boosts root libraries to find the probability of success from the cdf, given I know ans, the number of successes, and the number of trials?
You want the quantile:
http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/math_toolkit/dist_ref/nmp.html#math_toolkit.dist_ref.nmp.quantile
also known as the inverse cdf or the percent point function. Example of
use:
http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html
HTH, John.
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