boostmath (version 1.4.0)

geometric_distribution: Geometric Distribution Functions

Description

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

Usage

geometric_distribution(prob)
geometric_pdf(x, prob)
geometric_lpdf(x, prob)
geometric_cdf(x, prob)
geometric_lcdf(x, prob)
geometric_quantile(p, prob)
geometric_find_lower_bound_on_p(trials, alpha)
geometric_find_upper_bound_on_p(trials, alpha)
geometric_find_minimum_number_of_trials(failures, prob, alpha)
geometric_find_maximum_number_of_trials(failures, 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

prob

probability of success (0 < prob < 1)

x

quantile (non-negative integer)

p

probability (0 <= p <= 1)

trials

number of trials

alpha

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

failures

number of failures

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Geometric distribution with probability of success prob = 0.5
dist <- geometric_distribution(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
geometric_pdf(3, 0.5)
geometric_lpdf(3, 0.5)
geometric_cdf(3, 0.5)
geometric_lcdf(3, 0.5)
geometric_quantile(0.5, 0.5)
if (FALSE) {
# Find lower bound on p given 5 trials with 95% confidence
geometric_find_lower_bound_on_p(5, 0.05)
# Find upper bound on p given 5 trials with 95% confidence
geometric_find_upper_bound_on_p(5, 0.05)
# Find minimum number of trials to observe 3 failures with p = 0.5 at 95% confidence
geometric_find_minimum_number_of_trials(3, 0.5, 0.05)
# Find maximum number of trials to observe 3 failures with p = 0.5 at 95% confidence
geometric_find_maximum_number_of_trials(3, 0.5, 0.05)
}