Quantile function of the GEP, EP and PE distributions {geppe}

Quantile function of the GEP, EP and PE distributions

Description

Quantile function of the GEP, EP and PE distributions.

Usage

qepois(p, beta, lambda)
qgep(p, beta, alpha, lambda)
qpe(p, theta, lambda)

Arguments

p

A numerical vector with probability values.

beta

A strictly positive number, the scale parameter (\beta).

alpha

A stritly positive number, the \alpha parameter of the GEP distribution. If a=1, then one ends up with the EP distribution.

theta

A strictly positive number, the shape parameter (\theta).

lambda

A strictly positive number, the shape parameter (\lambda).

Details

The quantiles of the GEP, EP and PE distributions are computed.

The quantile function of the EP is given by x_q=-\dfrac{\log\left[\lambda^{-1}\log\left(q\left(1-e^{\lambda}\right)+e^{\lambda}\right)\right]}{\beta}.

The quantile function of the GEP is given by x_q=-\dfrac{\log{\left[1+\lambda^{-1}\log{\left(1-q^{1/\alpha}\left(1-e^{-\lambda}\right)\right)}\right]}}{\beta}.

The quantile function of the PE is given by x_q=\dfrac{\log{\left(\theta\right)}-\log{\left[-\log{\left(q-e^{\theta}\left(q-1\right)\right)}\right]}}{\lambda}.

Value

A vector with the quantile values.

Author(s)

Sofia Piperaki.

R implementation and documentation: Sofia Piperaki [e-mail] and Michail Tsagris [e-mail].

References

Barreto-Souza W. and Cribari-Neto F. (2009). A generalization of the exponential-Poisson distribution. Statistics and Probability Letters, 79(24): 2493–2500.

Louzada F., Ramos P. L. and Ferreira H. P. (2020). Exponential-Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence. Communications in Statistics-Simulation and Computation, 49(4): 1024–1043.

Rodrigues G. C., Louzada F. and Ramos P. L. (2018). Poisson-exponential distribution: different methods of estimation. Journal of Applied Statistics, 45(1): 128–144.

See Also

rgep, pgep

Examples

y <- qgep(seq(0.1, 0.9, by = 0.1), 1, 2, 3)