# ReversalPowerNormal: The Reversal Power Normal Distribution In powdist: Power and Reversal Power Distributions

## Description

Density, distribution function, quantile function and random generation for the reversal power normal distribution with parameters mu, sigma and lambda.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```drpnorm(x, lambda = 1, mu = 0, sigma = 1, log = FALSE) prpnorm(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qrpnorm(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rrpnorm(n, lambda = 1, mu = 0, sigma = 1) ```

## Arguments

 `x, q` vector of quantiles. `lambda` shape parameter. `mu, sigma` location and scale parameters. `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 reversal power Normal distribution has density

f(x)=[λ/σ][exp(-((x-μ)/σ)^2)/√(2π)][Φ(-(x-μ)/σ)]^(λ-1),

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

## References

Anyosa, S. A. C. (2017) Binary regression using power and reversal power links. Master's thesis in Portuguese. Interinstitutional Graduate Program in Statistics. Universidade de São Paulo - Universidade Federal de São Carlos. Available in https://repositorio.ufscar.br/handle/ufscar/9016.

Bazán, J. L., Torres -Avilés, F., Suzuki, A. K. and Louzada, F. (2017) Power and reversal power links for binary regressions: An application for motor insurance policyholders. Applied Stochastic Models in Business and Industry, 33(1), 22-34.

Bazán, J. L., Romeo, J. S. and Rodrigues, J. (2014) Bayesian skew-probit regression for binary response data. Brazilian Journal of Probability and Statistics. 28(4), 467–482.

## Examples

 ```1 2 3 4``` ```drpnorm(1, 1, 3, 4) prpnorm(1, 1, 3, 4) qrpnorm(0.2, 1, 3, 4) rrpnorm(5, 2, 3, 4) ```

### Example output

```[1] 0.08801633
[1] 0.3085375
[1] -0.3664849
[1]  0.913075  1.130731 -2.020498  1.121421  4.719563
```

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