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
)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).
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
# Chi-Squared distribution with 3 degrees of freedom
dist <- chi_squared_distribution(3)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.08110859
logcdf(dist, 0.5)
#> [1] -2.511966
pdf(dist, 0.5)
#> [1] 0.2196956
logpdf(dist, 0.5)
#> [1] -1.515512
hazard(dist, 0.5)
#> [1] 0.2390877
chf(dist, 0.5)
#> [1] 0.08458732
mean(dist)
#> [1] 3
median(dist)
#> [1] 2.365974
mode(dist)
#> [1] 1
range(dist)
#> [1] 0 Inf
quantile(dist, 0.2)
#> [1] 1.005174
standard_deviation(dist)
#> [1] 2.44949
support(dist)
#> [1] 0.000000e+00 1.797693e+308
variance(dist)
#> [1] 6
skewness(dist)
#> [1] 1.632993
kurtosis(dist)
#> [1] 7
kurtosis_excess(dist)
#> [1] 4
# Convenience functions
chi_squared_pdf(2, 3)
#> [1] 0.2075537
chi_squared_lpdf(2, 3)
#> [1] -1.572365
chi_squared_cdf(2, 3)
#> [1] 0.4275933
chi_squared_lcdf(2, 3)
#> [1] -0.8495828
chi_squared_quantile(0.5, 3)
#> [1] 2.365974
# 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)
#> [1] 106.0113