Density computation of the GEP, EP and PE distributions {geppe}

Density computation of the GEP, EP and PE distributions

Description

Density computation of the GEP, EP and PE distributions.

Usage

depois(x, beta, lambda, logged = FALSE)
dgep(x, beta, alpha, lambda, logged = FALSE)
dpe(x, theta, lambda, logged = FALSE)

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).

logged

Should the logarithm of the density values be computed? The default value is FALSE.

Details

The density values of the GEP, EP and PE distributions are computed. The density function of the EP is given by f(x)=\dfrac{\lambda \beta e^{-\lambda-\beta x + \lambda e^{-\beta x}}}{1-e^{-\lambda}}.

The density function of the GEP is given by f(x)=\dfrac{\alpha \lambda \beta}{\left(1-e^{-\lambda}\right)^{\alpha}}\left(1-e^{-\lambda+\lambda e^{-\beta x}}\right)^{\alpha-1}e^{-\lambda -\beta x + \lambda e^{-\beta x}}.

The density function of the PE is given by f(x)=\dfrac{\theta \lambda e^{-\lambda x-\theta e^{\lambda x}}}{1-e^{-\theta}}.

Value

A vector with the (logged) 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

rgep, pgep

Examples

x <- rgep(100, 1, 2, 3)
y <- dgep(x, 1, 2, 3, logged = TRUE)
sum(y)