MPS: An R package for modelling shifted families of distributions

Abstract

Generalised statistical distributions have been widely used over the last decades for modelling phenomena in different fields. The generalisations have been made to produce distributions with more flexibility and lead to more accurate modelling in practice. Statistical analysis of the generalised distributions requires new statistical packages. The Newdistns package due to Nadarajah and Rocha provides R routines with functionality to compute probability density function (PDF), cumulative distribution function (CDF), quantile function, random numbers and parameter estimates of 19 families of distributions with applications in survival analysis. Here, we introduce an R package, called MPS, for computing PDF, CDF, quantile function, random numbers, Q–Q plots and parameter estimates for 24 shifted new families of distributions. By considering an extra location parameter, each family will be defined on the whole real line and so covers a broader range of applicability. We adopt the well-known maximum product spacing approach to estimate parameters of the families because under some situations the maximum likelihood (ML) estimators fail to exist. We demonstrate MPS by analysing two well-known real data sets. For the first data set, the ML estimators break down, but MPS works well. For the second set, adding a location parameter results in a reasonable model while the absence of the location parameter makes the model quite inappropriate. The MPS is available from CRAN at https://cran.r-project.org/package=MPS.