# PowerT: The Power Student t Distribution In powdist: Power and Reversal Power Distributions

## Description

Density, distribution function, quantile function and random generation for the power Student t distribution with parameters mu, sigma, lambda and df.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```dpt(x, lambda = 1, mu = 0, sigma = 1, df, log = FALSE) ppt(q, lambda = 1, mu = 0, sigma = 1, df, lower.tail = TRUE, log.p = FALSE) qpt(p, lambda = 1, mu = 0, sigma = 1, df, lower.tail = TRUE, log.p = FALSE) rpt(n, lambda = 1, mu = 0, sigma = 1, df) ```

## Arguments

 `x, q` vector of quantiles. `lambda` shape parameter. `mu, sigma` location and scale parameters. `df` degrees of freedom (> 0, maybe non-integer). df = Inf is allowed. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x ], otherwise, P[X > x]. `p` vector of probabilities. `n` number of observations.

## Details

The power Student t distribution has density

f(x)=[λ/σ][f((x-μ)/σ)][F((x-μ)/σ)] ^(λ-1),

where -∞<μ<∞ is the location paramether, σ^2>0 the scale parameter and λ>0 the shape parameter.

## References

Lemonte A. and Bazán J.L.

## Examples

 ```1 2 3 4``` ```dpt(1, 1, 3, 4, 1) ppt(1, 1, 3, 4, 1) qpt(0.2, 1, 3, 4, 1) rpt(5, 2, 3, 4, 1) ```

### Example output

``` 0.06366198
 0.3524164
 -2.505528
  2.9198734  2.0346696 30.1499991  5.9767464  0.7024134
```

powdist documentation built on May 1, 2019, 10:11 p.m.