cpd: An R Package for Complex Pearson Distributions

The complex Pearson (CP) distributions are a family of probability models for count data generated by the Gaussian hypergeometric function with complex arguments. The complex triparametric Pearson (CTP) distribution and its biparametric versions, the complex biparametric Pearson (CBP) and the extended biparametric Waring (EBW) distributions, belong to this family. They all have explicit expressions of the probability mass function (pmf), probability generating function and moments, so they are easy to handle from a computational point of view. Moreover, the CTP and EBW distributions can model over- and underdispersed count data, whereas the CBP can only handle overdispersed data, but unlike other well-known overdispersed distributions, the overdispersion is not due to an excess of zeros but other low values of the variable. Finally, the EBW distribution allows the variance to be split into three uniquely identifiable components: randomness, liability and proneness. These properties make the CP distributions of interest in the modeling of a great variety of data. For this reason, and for trying to spread their use, we have implemented an R package called cpd that contains the pmf, distribution function, quantile function and random generation for these distributions. In addition, the package contains fitting functions according to the maximum likelihood. This package is available from the Comprehensive R Archive Network (CRAN). In this work, we describe all the functions included in the cpd package, and we illustrate their usage with several examples. Moreover, the release of a plugin in order to use the package from the interface R Commander tries to contribute to the spreading of these models among non-advanced users

cpd: An R Package for Complex Pearson Distributions

The complex Pearson (CP) distributions are a family of probability models for count data generated by the Gaussian hypergeometric function with complex arguments. The complex triparametric Pearson (CTP) distribution and its biparametric versions, the complex biparametric Pearson (CBP) and the extended biparametric Waring (EBW) distributions, belong to this family. They all have explicit expressions of the probability mass function (pmf), probability generating function and moments, so they are easy to handle from a computational point of view. Moreover, the CTP and EBW distributions can model over- and underdispersed count data, whereas the CBP can only handle overdispersed data, but unlike other well-known overdispersed distributions, the overdispersion is not due to an excess of zeros but other low values of the variable. Finally, the EBW distribution allows the variance to be split into three uniquely identifiable components: randomness, liability and proneness. These properties make the CP distributions of interest in the modeling of a great variety of data. For this reason, and for trying to spread their use, we have implemented an R package called cpd that contains the pmf, distribution function, quantile function and random generation for these distributions. In addition, the package contains fitting functions according to the maximum likelihood. This package is available from the Comprehensive R Archive Network (CRAN). In this work, we describe all the functions included in the cpd package, and we illustrate their usage with several examples. Moreover, the release of a plugin in order to use the package from the interface R Commander tries to contribute to the spreading of these models among non-advanced users

GWRM: An R Package for Identifying Sources of Variation in Overdispersed Count Data

<div><p>Understanding why a random variable is actually random has been in the core of Statistics from its beginnings. The generalized Waring regression model for count data explains that inherent variability is given by three possible sources: randomness, liability and proneness. The model extends the negative binomial regression model and it is not included in the family of generalized linear models. In order to avoid that shortcoming, we developed the GWRM R package for fitting, describing and validating the model. The version we introduce in this communication provides a new design of the modelling function as well as new methods operating on the associated fitted model objects, so that the new software integrates easily into the computational toolbox for modelling count data in R. The release of a plug-in in order to use the package from the interface R Commander tries to contribute to the spreading of the model among non-advanced users. We illustrate the usage and the possibilities of the software with two examples from the fields of health and sport.</p></div

Installing the GWRM plugin for R Commander.

<p>Installing the GWRM plugin for R Commander.</p

The <i>GWRM</i> option <i>partition of variance</i> and its dialog box.

<p>The <i>GWRM</i> option <i>partition of variance</i> and its dialog box.</p

Simulated envelope of the residuals of the <i>GWRM</i> fit to goals data.

<p>Plot of the Pearson residuals against the order statistics of the normal distribution from the <i>GWRM</i> fitted to the goals scored by the footballers in the first division of the Spanish league in the 2004/2005 season.</p

<i>GWRM</i> parameter estimates.

<p>Each box plot summarizes the set of ten estimates of each parameter obtained from the fits of the ten season datasets.</p

The <i>GWRM</i> option <i>simulated envelope of residuals</i> and its dialog box.

<p>The <i>GWRM</i> option <i>simulated envelope of residuals</i> and its dialog box.</p

Simulated envelope of the residuals of the <i>GWRM</i> fit to badhealth data.

<p>Plot of the deviance residuals against the order statistics of the normal distribution from the <i>GWRM</i> fitted to the number of visits to doctor during 1998.</p

Proportion of the variance components for each position.

<p>Each boxplot summarizes the ten values of the variance partition component obtained from the fits of the ten season datasets.</p