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

Distribution function of the GEP, EP and PE distributions

Description

Distribution function of the GEP, EP and PE distributions.

Usage

pepois(x, beta, lambda)
pgep(x, beta, alpha, lambda)
ppe(x, theta, lambda)

Arguments

x

A numerical vector with non-negative 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 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}}.

Value

A vector with the cumulative distribution density 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

dgep, qgep

Examples

x <- rgep(100, 1, 2, 3)
y <- pgep(x, 1, 2, 3)