# Logistic {stats}

### 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 ` `

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 π^2 /3 s^2.

### Values

`dlogis`

gives the density, `plogis`

gives the distribution function, `qlogis`

gives the quantile function, and `rlogis`

generates random deviates. The length of the result is determined by `n`

for `rlogis`

, and is the maximum of the lengths of the numerical parameters for the other functions. The numerical parameters other than `n`

are recycled to the length of the result. Only the first elements of the logical parameters are used.

### 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.

### 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 a *sigmoid function* in contexts such as neural networks.

### See Also

Distributions for other standard distributions.

Documentation reproduced from R 3.0.2. License: GPL-2.