Quantile function of the GEP, EP and PE distributions {geppe} | R Documentation |
Quantile function of the GEP, EP and PE distributions.
qepois(p, beta, lambda)
qgep(p, beta, alpha, lambda)
qpe(p, theta, lambda)
p |
A numerical vector with probability values. |
beta |
A strictly positive number, the scale parameter ( |
alpha |
A stritly positive number, the |
theta |
A strictly positive number, the shape parameter ( |
lambda |
A strictly positive number, the shape parameter ( |
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}.
A vector with the quantile values.
Sofia Piperaki.
R implementation and documentation: Sofia Piperaki sofiapip23@gmail.com and Michail Tsagris mtsagris@uoc.gr.
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.
y <- qgep(seq(0.1, 0.9, by = 0.1), 1, 2, 3)