## 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.

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

The following R code demonstrates how to fit a multitype NonHomogeneous Poisson Process (NHPP) model to temporal data. Multitype Poisson processes belong to the family of marked point processes.

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 temporal data.

## R code for fitting a nonhomogeneous temporal Poisson process model using the spatstat package

In my previous blog post I showed how to fit power and loglinear nonhomogeneous Poisson process (NHPP) models to temporal data.

The following R code fits these same two models, but this time using the spatstat package.

## R code for fitting a nonhomogeneous temporal Poisson process model

The following R code demonstrates how to fit a nonhomogeneous Poisson process (NHPP) model to temporal data.

The R code may be used to fit 1) a NHPP model with a loglinear intensity function, with the intensity at time t defined by $e^{\gamma_{0} + \gamma_{1}t}$ , or 2) a NHPP model with a power law intensity function, with the intensity at time t defined by $\frac{\beta}{\eta}(\frac{t}{\eta})^{\beta-1}$. The latter NHPP model is sometimes referred to as the Crow-AMSAA model.

## 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