Probability theory is the foundation of statistics, and R has plenty of machinery for working with probability, probability distributions, and random variables. The recipes in this chapter show you how to calculate probabilities from quantiles, calculate quantiles from probabilities, generate random variables drawn from distributions, plot distributions, and so forth.

R has an abbreviated name for every probability distribution. This name is used to identify the functions associated with the distribution. For example, the name of the Normal distribution is “norm”, which is the root of these function names:

Function | Purpose |
---|---|

`dnorm` | Normal density |

`pnorm` | Normal distribution function |

`qnorm` | Normal quantile function |

`rnorm` | Normal random variates |

Table 8-1 describes some common discrete distributions, and Table 8-2 describes several common continuous distributions.

Table 8-1. Discrete distributions

Discrete distribution | R name | Parameters |
---|---|---|

Binomial | binom | n = number of trials; p = probability of success for one trial |

Geometric | geom | p = probability of success for one trial |

Hypergeometric | hyper | m = number of white balls in urn; n = number of black balls in urn; k = number of balls drawn from urn |

Negative binomial (NegBinomial) | nbinom | size = number of successful trials; either prob = probability of successful trial or mu = mean |

Poisson | pois | lambda = mean |

Table 8-2. Continuous distributions

Continuous distribution | R name | Parameters |
---|---|---|

Beta | beta | shape1; shape2 |

Cauchy | cauchy | location; ... |

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