PowerCauchy: The Power Cauchy Distribution In powdist: Power and Reversal Power Distributions

Description

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

Usage

 ```1 2 3 4 5 6 7 8 9``` ```dpcauchy(x, lambda = 1, mu = 0, sigma = 1, log = FALSE) ppcauchy(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qpcauchy(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rpcauchy(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 power Cauchy distribution has density

f(x)=[λ/σ][1/(π(1+(x-μ)/σ))][(1/π)arctan((x-μ)/σ)+(1/2)]^(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.

Examples

 ```1 2 3 4``` ```dpcauchy(1, 1, 3, 4) ppcauchy(1, 1, 3, 4) qpcauchy(0.2, 1, 3, 4) rpcauchy(5, 2, 3, 4) ```

Example output

```[1] 0.06366198
[1] 0.3524164
[1] -2.505528
[1]  8.3498455 -2.1810830  0.6116285  6.1357565  4.5858244
```

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