boostmath (version 1.4.0)

binomial_distribution: Binomial Distribution Functions

Description

Functions to compute the probability density function, cumulative distribution function, and quantile function for the Binomial distribution.

Usage

binomial_distribution(n, prob)
binomial_pdf(k, n, prob)
binomial_lpdf(k, n, prob)
binomial_cdf(k, n, prob)
binomial_lcdf(k, n, prob)
binomial_quantile(p, n, prob)
binomial_find_lower_bound_on_p(n, k, alpha, method = "clopper_pearson_exact")
binomial_find_upper_bound_on_p(n, k, alpha, method = "clopper_pearson_exact")
binomial_find_minimum_number_of_trials(k, prob, alpha)
binomial_find_maximum_number_of_trials(k, prob, alpha)

Value

A single numeric value with the computed probability density, log-probability density, cumulative distribution, log-cumulative distribution, or quantile depending on the function called.

Arguments

n

number of trials (n >= 0)

prob

probability of success on each trial (0 <= prob <= 1)

k

number of successes (0 <= k <= n)

p

probability (0 <= p <= 1)

alpha

Largest acceptable probability that the true value of the success fraction is less than the value returned (by binomial_find_lower_bound_on_p) or greater than the value returned (by binomial_find_upper_bound_on_p).

method

Method to use for calculating the confidence bounds. Options are "clopper_pearson_exact" (default) and "jeffreys_prior".

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Binomial distribution with n = 10, prob = 0.5
dist <- binomial_distribution(10, 0.5)
# Apply generic functions
cdf(dist, 2)
logcdf(dist, 2)
pdf(dist, 2)
logpdf(dist, 2)
hazard(dist, 2)
chf(dist, 2)
mean(dist)
median(dist)
mode(dist)
range(dist)
quantile(dist, 0.2)
standard_deviation(dist)
support(dist)
variance(dist)
skewness(dist)
kurtosis(dist)
kurtosis_excess(dist)

# Convenience functions
binomial_pdf(3, 10, 0.5)
binomial_lpdf(3, 10, 0.5)
binomial_cdf(3, 10, 0.5)
binomial_lcdf(3, 10, 0.5)
binomial_quantile(0.5, 10, 0.5)

if (FALSE) {
# Find lower bound on p given k = 3 successes in n = 10 trials with 95% confidence
binomial_find_lower_bound_on_p(10, 3, 0.05)
# Find upper bound on p given k = 3 successes in n = 10 trials with 95% confidence
binomial_find_upper_bound_on_p(10, 3, 0.05)
# Find minimum number of trials n to observe k = 3 successes with p = 0.5 at 95% confidence
binomial_find_minimum_number_of_trials(3, 0.5, 0.05)
# Find maximum number of trials n to observe k = 3 successes with p = 0.5 at 95% confidence
binomial_find_maximum_number_of_trials(3, 0.5, 0.05)
}