Logistic {stats} | R Documentation |

## The Logistic Distribution

### Description

Density, distribution function, quantile function and random
generation for the logistic distribution with parameters
`location`

and `scale`

.

### Usage

dlogis(x, location = 0, scale = 1, log = FALSE)
plogis(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qlogis(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rlogis(n, location = 0, scale = 1)

### Arguments

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If `length(n) > 1` , the length
is taken to be the number required. |

`location, scale` |
location and scale parameters. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`lower.tail` |
logical; if TRUE (default), probabilities are
*P[X <= x]*, otherwise, *P[X > x]*. |

### Details

If `location`

or `scale`

are omitted, they assume the
default values of `0`

and `1`

respectively.

The Logistic distribution with `location`

*= m* and
`scale`

*= s* has distribution function

*F(x) = 1 / (1 + exp(-(x-m)/s))*

and density

*f(x) = 1/s exp((x-m)/s) (1 + exp((x-m)/s))^-2.*

It is a long-tailed distribution with mean *m* and variance
*pi^2 /3 s^2*.

### Value

`dlogis`

gives the density,
`plogis`

gives the distribution function,
`qlogis`

gives the quantile function, and
`rlogis`

generates random deviates.

### Note

`qlogis(p)`

is the same as the well known ‘*logit*’
function, *logit(p) = log(p/(1-p))*, and `plogis(x)`

has
consequently been called the “inverse logit”.

The distribution function is a rescaled hyperbolic tangent,
`plogis(x) == (1+ tanh(x/2))/2`

, and it is called
*sigmoid function* in contexts such as neural networks.

### Source

`[dpr]logis`

are calculated directly from the definitions.

`rlogis`

uses inversion.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth & Brooks/Cole.

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
*Continuous Univariate Distributions*, volume 2, chapter 23.
Wiley, New York.

### Examples

var(rlogis(4000, 0, s = 5))# approximately (+/- 3)
pi^2/3 * 5^2

[Package

*stats* version 2.5.0

Index]