R: The t Distribution

t {nimble} | R 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)

[Package nimble version 0.10.0 Index]