dist.Bernoulli {LaplacesDemon} | R Documentation |

## Bernoulli Distribution

### Description

These functions provide the density, distribution function, quantile function, and random generation for the Bernoulli distribution.

### Usage

```
dbern(x, prob, log=FALSE)
pbern(q, prob, lower.tail=TRUE, log.p=FALSE)
qbern(p, prob, lower.tail=TRUE, log.p=FALSE)
rbern(n, prob)
```

### Arguments

`x` , `q` |
These are each a vector of quantiles. |

`p` |
This is a vector of probabilities. |

`n` |
This is the number of observations. If |

`prob` |
This is the probability of success on each trial. |

`log` , `log.p` |
Logical. if |

`lower.tail` |
Logical. if |

### Details

Application: Continuous Univariate

Density:

`p(\theta) = {p}^{\theta} {(1-p)}^{1-\theta}`

,`\theta = 0,1`

Inventor: Jacob Bernoulli

Notation 1:

`\theta \sim \mathcal{BERN}(p)`

Notation 2:

`p(\theta) = \mathcal{BERN}(\theta | p)`

Parameter 1: probability parameter

`0 \le p \le 1`

Mean:

`E(\theta) = p`

Variance:

`var(\theta) = \frac{p}{1-p}`

Mode:

`mode(\theta) =`

The Bernoulli distribution is a binomial distribution with
`n=1`

, and one instance of a Bernoulli distribution is called a
Bernoulli trial. One coin flip is a Bernoulli trial, for example. The
categorical distribution is the generalization of the Bernoulli
distribution for variables with more than two discrete values. The
beta distribution is the conjugate prior distribution of the Bernoulli
distribution. The geometric distribution is the number of Bernoulli
trials needed to get one success.

### Value

`dbern`

gives the density,
`pbern`

gives the distribution function,
`qbern`

gives the quantile function, and
`rbern`

generates random deviates.

### See Also

### Examples

```
library(LaplacesDemon)
dbern(1, 0.7)
rbern(10, 0.5)
```

*LaplacesDemon*version 16.1.6 Index]