Counting: permutations_count (N!, eq. 1.3), partial_permutations
(N!/(N-n)!, eq. 1.5), binomial_expansion (eq. 1.21), hockey_stick
(eq. 1.29). Events: classify_events (independence and exclusivity,
sec. 2.2.3), conditional_from_joint (P(B|A) = P(A and B)/P(A), eq.
2.48), conditional_subset (eq. 2.49). Moments: bernoulli_variance
(pq, eq. 3.22), binomial_variance (npq, eq. 3.33). Distributions:
binomial_pmf_vector (eq. 4.10), hypergeometric_pmf (eq. 4.71),
poisson_small_interval (eq. 4.18), poisson_mean_rate (eq. 4.19),
poisson_zero_series (eq. 4.53), density_expectation (trapezoid rule,
eq. 4.55), poisson_binomial_peak_ratio (eq. 4.98), the Gaussian
approximations gaussian_approx_2n, gaussian_approx_n,
gaussian_approx_biased (eqs. 5.13-5.15) and gaussian_sum_density
(eq. 6.70).
Usage
bernoulli_variance(p)
binomial_expansion(a, b, n)
binomial_pmf_vector(n, p)
binomial_variance(n, p)
classify_events(p_a, p_b, p_ab, tol = 1e-12)
conditional_from_joint(p_a_and_b, p_a)
conditional_subset(p_b, p_a)
density_expectation(grid, density)
gaussian_approx_2n(x, n)
gaussian_approx_n(x, n)
gaussian_approx_biased(x, n, p)
gaussian_sum_density(z, sigma_x, sigma_y)
hockey_stick(n, k)
hypergeometric_pmf(k, N, K, n)
partial_permutations(N, n)
permutations_count(n)
poisson_binomial_peak_ratio(n, p)
poisson_mean_rate(lam, t)
poisson_small_interval(lam, eps)
poisson_zero_series(a, terms = 60)Arguments
- p, p_a, p_b, p_ab, p_a_and_b
Probabilities.
- a, b
Terms of the binomial, or the Poisson mean
a.- n, N, K, k
Non-negative integers.
- tol
Tolerance of the event classification.
- grid, density
Grid and density values.
- x
Deviation from the mean.
- z
Value of the sum.
- sigma_x, sigma_y
Standard deviations.
- lam
Rate.
- t
Duration.
- eps
Interval length.
- terms
Number of series terms.