unifres.fun: Calculate exponential and uniform (generalized) residuals of...
In NHPoisson: Modelling and Validation of Non Homogeneous Poisson Processes

Description Usage Arguments Details Value References See Also Examples

This function calculates the exponential d_i and the uniform (generalized) residuals u_i of a HPP, using the occurrence points t_i.

1	unifres.fun(posEH)

posEH

Numeric vector, the occurrence points of a HPP.

The exponential residuals of a HPP are defined as the inter-event distances d_i=t_i-t_{i-1}, that are an i.i.d. exponential sample. The series d_i is an example of the generalized residuals proposed by Cox and Snell (1968). The uniform residuals, defined as the function \exp(-d_i) of the exponential residuals, are an i.i.d. uniform sample, see Ogata (1988).

A list with elements

`expres`	Numeric vector of the exponential residuals.
`unires`	Numeric vector of the uniform residuals.
`posEH`	Input argument.

Abaurrea, J., Asin, J., Cebrian, A.C. and Centelles, A. (2007). Modeling and forecasting extreme heat events in the central Ebro valley, a continental-Mediterranean area. Global and Planetary Change, 57(1-2), 43-58.

Cebrian, A.C., Abaurrea, J. and Asin, J. (2015). NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes. Journal of Statistical Software, 64(6), 1-24.

Cox, D. R. and Snell, E. J. (1968). A general definition of residuals. Journal of the Royal Statistical Society, series B, 30(2), 248-275. 83(401), 9-27.

Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes.Journal of the American Statistical Association, 83(401), 9-27.

transfH.fun, graphresU.fun

## generates the occurrence times of a homogeneours PP with  constant intensity 0.01 
## and calculates de residuals

aux<-simNHP.fun(lambda=rep(0.01,1000))

res<-unifres.fun(aux$posNH)