To calculate probabilities for continuous distributions, you need to use the cumulative distribution function, CDF. Unlike discrete distributions, there is no single point probability, P(X=x), there is a density. In this article, we will learn how to calculate probabilities of continuous distributions in R.

To calculate these probabilities, we can use function prefixed with `p`

for each distribution. For example, to calculate the cdf of the normal
distribution, we can use `pnorm`

.

`pnorm(q = .8, mean = 0, sd = 1)`

`## [1] 0.7881446`

This calculates the probability of selecting an item below .8 in the normal distribution.

Next, we can take a look at getting the quantile from a distribution.
This is also known as the inverse CDF. To do this, we can use the
distribution functions prefixed with a `q`

. In our case, we will use
`qninom`

.

`qnorm(0.7881446, mean = 0, sd = 1)`

`## [1] 0.8`

Notice that our result is .8 which is exactly the value of `q`

from the
previous section. This shows how the two functions are inversely
related.

It is common to generate a random sample of normal variables. These are
used in simulations and many other situations you will learn. To do
this, we can follow a similar pattern of the above function using the
`norm`

preceded by a `r`

for random.

`rnorm(10)`

```
## [1] 0.86408802 -0.50945900 0.84883333 0.37336024 1.43838537 1.11448386
## [7] 0.46681953 0.75352516 0.25414154 0.09360259
```

Here we generated sample of size 10 from the normal distributions.

The pdf isnâ€™t very useful for continuous variables as you are usually
looking for the probability which is the cumulative density. However,
you can use the `dnorm`

and other functions to generate the density
plots.

```
x <- seq(-4, 4, length=100)
y <- dnorm(x)
plot(y, type='l')
```

R provides many other continuous distributions with the same structure as above. Here is a list of many distributions and their respective functions.

Distribution | Functions | |||
---|---|---|---|---|

Beta | pbeta | qbeta | dbeta | rbeta |

Binomial | pbinom | qbinom | dbinom | rbinom |

Cauchy | pcauchy | qcauchy | dcauchy | rcauchy |

Chi-Square | pchisq | qchisq | dchisq | rchisq |

Exponential | pexp | qexp | dexp | rexp |

F | pf | qf | df | rf |

Gamma | pgamma | qgamma | dgamma | rgamma |

Geometric | pgeom | qgeom | dgeom | rgeom |

Hypergeometric | phyper | qhyper | dhyper | rhyper |

Logistic | plogis | qlogis | dlogis | rlogis |

Log Normal | plnorm | qlnorm | dlnorm | rlnorm |

Negative Binomial | pnbinom | qnbinom | dnbinom | rnbinom |

Normal | pnorm | qnorm | dnorm | rnorm |

Poisson | ppois | qpois | dpois | rpois |

Student t | pt | qt | dt | rt |

Studentized Range | ptukey | qtukey | dtukey | rtukey |

Uniform | punif | qunif | dunif | runif |

Weibull | pweibull | qweibull | dweibull | rweibull |

Wilcoxon Rank Sum Statistic | pwilcox | qwilcox | dwilcox | rwilcox |

Wilcoxon Signed Rank Statistic | psignrank | qsignrank | dsignrank | rsignrank |