t: The t Distribution

In nimble: MCMC, Particle Filtering, and Programmable Hierarchical Modeling

The t Distribution

Description

Density, distribution function, quantile function and random generation for the t distribution with df degrees of freedom, allowing non-zero location, mu, and non-unit scale, sigma

Usage

dt_nonstandard(x, df = 1, mu = 0, sigma = 1, log = FALSE)

rt_nonstandard(n, df = 1, mu = 0, sigma = 1)

pt_nonstandard(q, df = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

qt_nonstandard(p, df = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

x	vector of values.
df	vector of degrees of freedom values.
mu	vector of location values.
sigma	vector of scale values.
log	logical; if TRUE, probability density is returned on the log scale.
n	number of observations.
q	vector of quantiles.
lower.tail	logical; if TRUE (default) probabilities are P[X \le x]; otherwise, P[X > x].
log.p	logical; if TRUE, probabilities p are given by user as log(p).
p	vector of probabilities.

Details

See Gelman et al., Appendix A or the BUGS manual for mathematical details.

Value

dt_nonstandard gives the density, pt_nonstandard gives the distribution function, qt_nonstandard gives the quantile function, and rt_nonstandard generates random deviates.

Author(s)

Christopher Paciorek

References

Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2004) Bayesian Data Analysis, 2nd ed. Chapman and Hall/CRC.

See Also

Distributions for other standard distributions

Examples

x <- rt_nonstandard(50, df = 1, mu = 5, sigma = 1)
dt_nonstandard(x, 3, 5, 1)

nimble documentation built on Sept. 11, 2024, 7:10 p.m.