boostmath (version 1.4.0)

chi_squared_distribution: Chi-Squared Distribution Functions

Description

Functions to compute the probability density function, cumulative distribution function, and quantile function for the Chi-Squared distribution.

Usage

chi_squared_distribution(df)
chi_squared_pdf(x, df)
chi_squared_lpdf(x, df)
chi_squared_cdf(x, df)
chi_squared_lcdf(x, df)
chi_squared_quantile(p, df)
chi_squared_find_degrees_of_freedom(
  difference_from_variance,
  alpha,
  beta,
  variance,
  hint = 100
)

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

df

degrees of freedom (df > 0)

x

quantile

p

probability (0 <= p <= 1)

difference_from_variance

The difference from the assumed nominal variance that is to be detected: Note that the sign of this value is critical (see the documentation for more details).

alpha

The acceptable probability of a Type I error (false positive).

beta

The acceptable probability of a Type II error (false negative).

variance

The assumed nominal variance.

hint

An initial guess for the degrees of freedom to start the search from (current sample size is a good start).

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Chi-Squared distribution with 3 degrees of freedom
dist <- chi_squared_distribution(3)
# 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
chi_squared_pdf(2, 3)
chi_squared_lpdf(2, 3)
chi_squared_cdf(2, 3)
chi_squared_lcdf(2, 3)
chi_squared_quantile(0.5, 3)

# Find degrees of freedom needed to detect a difference from variance of 2.0
# with alpha = 0.05 and beta = 0.2 when the nominal variance is 5.0
chi_squared_find_degrees_of_freedom(2.0, 0.05, 0.2, 5.0)