nimble (version 1.2.1)

t: 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)

Value

dt_nonstandard gives the density, pt_nonstandard gives the distribution function, qt_nonstandard gives the quantile function, and rt_nonstandard

generates random deviates.

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.

Author

Christopher Paciorek

Details

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

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)