R code for fitting a multitype NHPP model to grouped temporal data

The following R code demonstrates how to fit a multitype NonHomogeneous Poisson Process (NHPP) model to grouped temporal data. Multitype Poisson processes belong to the family of marked point processes.
Note that grouped temporal data occurs when only the number of recurrences within a given time interval are known.

The R code may be used to fit 1) a multitype NHPP model with a loglinear intensity function, with the intensity at time t defined by  e^{\gamma_{0} + \gamma_{1}t}, or 2) a multitype NHPP model with a power law intensity function, with the intensity at time t defined by  \gamma_{0}*t^{\gamma_{1}}.

Furthermore, the R code also shows how to fit a multitype Homogeneous Poisson Process (HPP) model to grouped temporal data.

NHPP multitype grouped

Continue reading R code for fitting a multitype NHPP model to grouped temporal data

R code for fitting a loglinear-NHPP model to grouped temporal data

The following R code fits a NonHomogeneous Poisson Process (NHPP) model to grouped temporal data. Grouped temporal data occurs when only the number of recurrences within a given time interval are known.
The R code fits a NHPP model with a loglinear intensity function, where the intensity at time t is given by e^{\gamma_{0} + \gamma_{1}t} .
NHPP loglikelihood Continue reading R code for fitting a loglinear-NHPP model to grouped temporal data

R code for fitting the Crow-AMSAA model to grouped data

The Crow-AMSAA model is frequently used for analyzing and assessing reliability growth. In case of grouped data the Crow-AMSAA model parameters have to be estimated by numerical optimization. Grouped data occurs when only the number of failures within a given time period are known.

The Crow-AMSAA model in the R code fits a NonHomogenous Poisson Process (NHPP) having a power law intensity function. See this post for fitting a NHPP model having a loglinear intensity function. Continue reading R code for fitting the Crow-AMSAA model to grouped data