exp: The Exponential distribution

In distributionsrd: Distribution Fitting and Evaluation

Description

Raw moments for the exponential distribution.

Usage

mexp(r = 0, truncation = 0, rate = 1, lower.tail = TRUE)

Arguments

r	rth raw moment of the distribution, defaults to 1.
truncation	lower truncation parameter, defaults to 0.
rate	rate of the distribution with default values of 1.
lower.tail	logical; if TRUE (default), moments are E[x^r|X ≤ y], otherwise, E[x^r|X > y]

Details

Probability and Cumulative Distribution Function:

f(x) = \frac{1}{s}e^{-\frac{ω}{s}} , \qquad F_X(x) = 1-e^{-\frac{ω}{s}}

The y-bounded r-th raw moment of the distribution equals:

s^{σ_s - 1} Γ≤ft(σ_s +1, \frac{y}{s} \right)

where Γ(,) denotes the upper incomplete gamma function.

Value

Returns the truncated rth raw moment of the distribution.

Examples

## The zeroth truncated moment is equivalent to the probability function
pexp(2, rate = 1)
mexp(truncation = 2)

## The (truncated) first moment is equivalent to the mean of a (truncated) random sample,
#for large enough samples.
x <- rexp(1e5, rate = 1)
mean(x)
mexp(r = 1, lower.tail = FALSE)

sum(x[x > quantile(x, 0.1)]) / length(x)
mexp(r = 1, truncation = quantile(x, 0.1), lower.tail = FALSE)

distributionsrd documentation built on July 1, 2020, 10:21 p.m.