Distribution function of the GEP, EP and PE distributions {geppe} | R Documentation |
Distribution function of the GEP, EP and PE distributions.
pepois(x, beta, lambda)
pgep(x, beta, alpha, lambda)
ppe(x, theta, lambda)
x |
A numerical vector with non-negative 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 cumulative distribution values of the GEP, EP and PE distributions are computed.
The probability function of the EP is given by
f(x)=\dfrac{e^{\lambda e^{-\beta x}}}{1-e^{\lambda}}.
The probability function of the GEP is given by
f(x)=\left(\dfrac{1-e^{-\lambda+\lambda e^{-\beta x}}}{1-e^{-\lambda}}\right)^{\alpha]}.
The probability function of the PE is given by
f(x)=\dfrac{1-e^{\theta-\theta e^{-\lambda x}}}{1-e^{-\theta}}.
A vector with the cumulative distribution density 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.
x <- rgep(100, 1, 2, 3)
y <- pgep(x, 1, 2, 3)