tExp function

The truncated exponential distribution

Density, distribution function, quantile function and random generation for the truncated exponential distribution.

dtexp(x, rate = 1, endpoint = Inf, log = FALSE)
ptexp(x, rate = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtexp(p, rate = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtexp(n, rate = 1, endpoint = Inf)

Arguments

• x: Vector of quantiles.
• p: Vector of probabilities.
• n: Number of observations.
• rate: The rate parameter for the exponential distribution, default is 1.
• endpoint: Endpoint of the truncated exponential distribution. The default value is Inf for which the truncated exponential distribution corresponds to the ordinary exponential distribution.
• log: Logical indicating if the densities are given as $\log(f)$, default is FALSE.
• lower.tail: Logical indicating if the probabilities are of the form $P(X\le x)$ (TRUE) or $P(X>x)$ (FALSE). Default is TRUE.
• log.p: Logical indicating if the probabilities are given as $\log(p)$, default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the truncated exponential distribution is equal to $F_T(x) = F(x) / F(T)$ for $x \le T$ where $F$ is the CDF of the ordinary exponential distribution and $T$ is the endpoint (truncation point) of the truncated exponential distribution.

Returns

dtexp gives the density function evaluated in $x$, ptexp the CDF evaluated in $x$ and qtexp the quantile function evaluated in $p$. The length of the result is equal to the length of $x$ or $p$.

rtexp returns a random sample of length $n$.

Author(s)

Tom Reynkens.

See Also

Exponential, Distributions

Examples

# Plot of the PDF
x <- seq(0, 10, 0.01)
plot(x, dtexp(x, rate = 2, endpoint=5), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(0, 10, 0.01)
plot(x, ptexp(x, rate = 2, endpoint=5), xlab="x", ylab="CDF", type="l")