Logistic {stats}

The Logistic Distribution
Package:
stats
Version:
R 3.0.2

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.

```var(rlogis(4000, 0, scale = 5))  # approximately (+/- 3)