ReversalPowerCauchy: The Reversal Power Cauchy Distribution

Description Usage Arguments Details References Examples

Description

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

Usage

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drpcauchy(x, lambda = 1, mu = 0, sigma = 1, log = FALSE)

prpcauchy(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)

qrpcauchy(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)

rrpcauchy(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 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 S<c3><a3>o Paulo - Universidade Federal de S<c3><a3>o Carlos. Available in https://repositorio.ufscar.br/handle/ufscar/9016.

Baz<c3><a1>n, J. L., Torres -Avil<c3><a9>s, 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

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drpcauchy(1, 1, 3, 4)
prpcauchy(1, 1, 3, 4)
qrpcauchy(0.2, 1, 3, 4)
rrpcauchy(5, 2, 3, 4)

susanca/powdist documentation built on May 24, 2019, 7:20 a.m.