# tlogis: The Truncated Logistic Distribution In crch: Censored Regression with Conditional Heteroscedasticity

 tlogis R Documentation

## The Truncated Logistic Distribution

### Description

Density, distribution function, quantile function, and random generation for the left and/or right truncated logistic distribution.

### Usage

```dtlogis(x, location = 0, scale = 1, left = -Inf, right = Inf, log = FALSE)

ptlogis(q, location = 0, scale = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)

qtlogis(p, location = 0, scale = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)

rtlogis(n, location = 0, scale = 1, left = -Inf, right = Inf)
```

### 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` location parameter. `scale` scale parameter. `left` left truncation point. `right` right truncation point. `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 not specified they assume the default values of `0` and `1`, respectively. `left` and `right` have the defaults `-Inf` and `Inf` respectively.

The truncated logistic distribution has density

f(x) = 1/σ λ((x - μ)/σ) / (Λ((right - μ)/σ) - Λ((left - μ)/σ))

for left ≤ x ≤ right, and 0 otherwise.

Λ and λ are the cumulative distribution function and probability density function of the standard logistic distribution respectively, μ is the location of the distribution, and σ the scale.

### Value

`dtlogis` gives the density, `ptlogis` gives the distribution function, `qtlogis` gives the quantile function, and `rtlogis` generates random deviates.

`dlogis`