# t: The t Distribution In nimble: MCMC, Particle Filtering, and Programmable Hierarchical Modeling

 t 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.

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