boostmath (version 1.4.0)

students_t_distribution: Student's T Distribution Functions

Description

Functions to compute the probability density function, cumulative distribution function, and quantile function for the Student's t distribution.

Usage

students_t_distribution(df = 1)
students_t_pdf(x, df = 1)
students_t_lpdf(x, df = 1)
students_t_cdf(x, df = 1)
students_t_lcdf(x, df = 1)
students_t_quantile(p, df = 1)
students_t_find_degrees_of_freedom(
  difference_from_mean,
  alpha,
  beta,
  sd,
  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 (default is 1)

x

quantile

p

probability (0 <= p <= 1)

difference_from_mean

The difference from the assumed nominal mean that is to be detected.

alpha

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

beta

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

sd

The assumed standard deviation.

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

# Student's t distribution with 5 degrees of freedom
dist <- students_t_distribution(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
students_t_pdf(0, 5)
students_t_lpdf(0, 5)
students_t_cdf(0, 5)
students_t_lcdf(0, 5)
students_t_quantile(0.5, 5)

# Find degrees of freedom needed to detect a difference from mean of 2.0
# with alpha = 0.05 and beta = 0.2 when the standard deviation is 3.0
students_t_find_degrees_of_freedom(2.0, 0.05, 0.2, 3.0)