scipy.special.bdtrin#

scipy.special.bdtrin(k, y, p, out=None) = <ufunc 'bdtrin'>#

Inverse function to bdtr with respect to n.

Finds the number of events n such that the sum of the terms 0 through k of the Binomial probability density for events with probability p is equal to the given cumulative probability y.

Parameters:

karray_like: Number of successes (float).
yarray_like: Cumulative probability (probability of k or fewer successes in n events).
parray_like: Success probability (float).
outndarray, optional: Optional output array for the function values

Returns:

nscalar or ndarray: The number of events n such that bdtr(k, n, p) = y.

See also

bdtr

Notes

This function uses the find_minimum_number_of_trials method of the binomial_distribution class of the Boost.Math C++ library [1].

References

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

How often do we have to flip a fair coin to have at least a 90% chance of getting 10 heads? bdtrin answers this question:

>>> import scipy.special as sc
>>> k = 10  # number of times we want heads
>>> p = 0.5  # probability of flipping heads
>>> y = 0.9  # cumulative probability
>>> result = sc.bdtrin(k, y, p)
>>> result
15.90442928275109

To verify, compute the cumulative probability of getting 10 or fewer successes in 16 trials with probability 0.5 using the binomial distribution from scipy.stats. Since bdtrin returns a non-integer number of trials, we round up to the next integer:

>>> from scipy.stats import Binomial
>>> Binomial(n=16, p=p).cdf(k)
0.8949432373046875