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

What is the largest number of times we can flip a fair coin and still have at least a 90% chance of getting 10 or fewer heads? bdtrin answers this question:

>>> import scipy.special as sc
>>> k = 10  # maximum number of heads
>>> p = 0.5  # probability of flipping heads
>>> y = 0.9  # cumulative probability
>>> result = sc.bdtrin(k, y, p)
>>> result
np.float64(15.90442928275109)

To verify, compute the cumulative probability of getting 10 or fewer successes in 15 trials with probability 0.5 using the binomial distribution from scipy.stats. Since the cumulative probability decreases as the number of trials increases, we round down to the nearest integer:

>>> from scipy.stats import Binomial
>>> Binomial(n=15, p=p).cdf(k)
np.float64(0.940765380859375)