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Binomial Distribution Functions

Source: R/binomial_distribution.R
binomial_distribution.Rd

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)

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".

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

# Binomial distribution with n = 10, prob = 0.5
dist <- binomial_distribution(10, 0.5)
# Apply generic functions
cdf(dist, 2)
#> [1] 0.0546875
logcdf(dist, 2)
#> [1] -2.90612
pdf(dist, 2)
#> [1] 0.04394531
logpdf(dist, 2)
#> [1] -3.124809
hazard(dist, 2)
#> [1] 0.0464876
chf(dist, 2)
#> [1] 0.05623972
mean(dist)
#> [1] 5
median(dist)
#> [1] 5
mode(dist)
#> [1] 5
range(dist)
#> [1]  0 10
quantile(dist, 0.2)
#> [1] 3
standard_deviation(dist)
#> [1] 1.581139
support(dist)
#> [1]  0 10
variance(dist)
#> [1] 2.5
skewness(dist)
#> [1] 0
kurtosis(dist)
#> [1] 2.8
kurtosis_excess(dist)
#> [1] -0.2

# Convenience functions
binomial_pdf(3, 10, 0.5)
#> [1] 0.1171875
binomial_lpdf(3, 10, 0.5)
#> [1] -2.14398
binomial_cdf(3, 10, 0.5)
#> [1] 0.171875
binomial_lcdf(3, 10, 0.5)
#> [1] -1.760988
binomial_quantile(0.5, 10, 0.5)
#> [1] 5

if (FALSE) { # \dontrun{
# 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)
} # }