Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite-dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models often seem out of reach for practitioners, as inference algorithms require careful design to handle the infinite number of parameters. The aim of this work is to facilitate the journey by providing computational tools for Bayesian nonparametric inference. The article describes a set of functions available in the R package BNPdensity for carrying out density estimation with an infinite mixture model, including all types of censored data. The package provides access to a large class of such models based on normalised random measures, which represent a generalisation of the popular Dirichlet process mixture. One striking advantage of this generalisation is that it offers much more robust priors on the number of clusters than the Dirichlet. Another crucial advantage is the complete flexibility in specifying the prior for the scale and location parameters of the clusters, because conjugacy is not required. Inference is performed using a theoretically grounded approximate sampling methodology known as the Ferguson & Klass algorithm. The package also offers several goodness-of-fit diagnostics, such as QQ plots, including a cross-validation criterion, the conditional predictive ordinate. The proposed methodology is illustrated using a classical ecological risk assessment method, known as the species sensitivity distribution problem, which showcases the benefits of the Bayesian nonparametric framework.