t: The t Distribution

tR Documentation

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 ≤ 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 March 18, 2022, 8:03 p.m.

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