negative_binomial_distribution: Negative Binomial Distribution Functions

In boostmath: 'R' Bindings for the 'Boost' Math Functions

Negative Binomial Distribution Functions

Description

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

Usage

negative_binomial_distribution(successes, success_fraction)

negative_binomial_pdf(x, successes, success_fraction)

negative_binomial_lpdf(x, successes, success_fraction)

negative_binomial_cdf(x, successes, success_fraction)

negative_binomial_lcdf(x, successes, success_fraction)

negative_binomial_quantile(p, successes, success_fraction)

negative_binomial_find_lower_bound_on_p(trials, successes, alpha)

negative_binomial_find_upper_bound_on_p(trials, successes, alpha)

negative_binomial_find_minimum_number_of_trials(
  failures,
  success_fraction,
  alpha
)

negative_binomial_find_maximum_number_of_trials(
  failures,
  success_fraction,
  alpha
)

Arguments

successes	number of successes (successes >= 0)
success_fraction	probability of success on each trial (0 <= success_fraction <= 1)
x	quantile
p	probability (0 <= p <= 1)
trials	number of trials
alpha	significance level (0 < alpha < 1)
failures	number of failures (failures >= 0)

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.

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Negative Binomial distribution with successes = 5, success_fraction = 0.5
dist <- negative_binomial_distribution(5, 0.5)
# Apply generic functions
cdf(dist, 0.5)
logcdf(dist, 0.5)
pdf(dist, 0.5)
logpdf(dist, 0.5)
hazard(dist, 0.5)
chf(dist, 0.5)
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
negative_binomial_pdf(3, 5, 0.5)
negative_binomial_lpdf(3, 5, 0.5)
negative_binomial_cdf(3, 5, 0.5)
negative_binomial_lcdf(3, 5, 0.5)
negative_binomial_quantile(0.5, 5, 0.5)

## Not run: 
# Find lower bound on p given 10 trials and 5 successes with 95% confidence
negative_binomial_find_lower_bound_on_p(10, 5, 0.05)
# Find upper bound on p given 10 trials and 5 successes with 95% confidence
negative_binomial_find_upper_bound_on_p(10, 5, 0.05)
# Find minimum number of trials to observe 3 failures with success fraction 0.5 at 95% confidence
negative_binomial_find_minimum_number_of_trials(3, 0.5, 0.05)
# Find maximum number of trials to observe 3 failures with success fraction 0.5 at 95% confidence
negative_binomial_find_maximum_number_of_trials(3, 0.5, 0.05)

## End(Not run)

boostmath documentation built on Dec. 15, 2025, 5:07 p.m.