One of the R language's most powerful features is its ability to deal with random distributions: not just generating random numbers from various distributions (based on a very powerful pseudo-random number generator), but also calculating densities, probabilities, and quintiles. John Cook provides a handy reference chart listing all of the distributions supported by standard R (reproduced below -- and there are many other distributions supported by contributed packages), and also explains the elegant naming scheme for the various functions.

Distribution |
Base name |
Parameters |

beta | `beta` |
`shape1` , `shape2, ncp` |

binomial | `binom` |
`size` , `prob` |

Cauchy | `cauchy` |
`location` , `scale` |

chi-squared | `chisq` |
`df, ncp` |

exponential | `exp` |
`rate` |

F | `f` |
`df1` , `df2, ncp` |

gamma | `gamma` |
`shape` , `rate` |

geometric | `geom` |
`p` |

hypergeometric | `hyper` |
`m` , `n` , `k` |

log-normal | `lnorm` |
`meanlog` , `sdlog` |

logistic | `logis` |
`location` , `scale` |

negative binomial | `nbinom` |
`size` , `prob` |

normal | `norm` |
`mean` , `sd` |

Poisson | `pois` |
`lambda` |

Student t | `t` |
`df, ncp` |

uniform | `unif` |
`min` , `max` |

Weibull | `weibull` |
`shape` , `scale` |

**Updated **Aug 20: added the ncp parameter to beta, chisq, f, and t with thanks to Doug Bates' comment below.

John D Cook: Distributions in R and S-PLUS

The argument lists in this table for the beta, chisq, f and t distributions are incomplete. R allows for a non-centrality parameter, ncp, in each of these distributions. (If I recall correctly, S-PLUS does not but I don't have a copy of that software available to check.)

Allowing for non-central versions of these distributions in R took a considerable amount of work, especially by Martin Maechler, and I think it should be acknowledged.

Posted by: Douglas Bates | August 20, 2010 at 06:49

Thanks for pointing that out Doug, I updated the post above. Martin and others from the R project definitely deserve a round of applause -- the accuracy of these functions, especially in the tails, is unparalleled. I didn't include some of the other parameters like lower.tail which give even more accuracy in some situations -- follow the links in the table to read up on the other options.

Posted by: David Smith | August 20, 2010 at 08:35