Description Usage Arguments Details Value Note References See Also Examples
Density, distribution function, quantile function, random generation and
moment-generating function (and its first two derivatives) for the
hypo-exponential distribution with rates rate
.
1 2 3 4 5 |
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
difforder |
the order of derivative for the moment-generating function; currently only implemented for 0, 1, 2. |
rate |
vector of (unique) rates. |
lower.tail |
logical; if |
log, log.p |
logical; if |
tailarea |
logical; if |
interval |
Passed to |
The sum of n independent exponentially distributed random variables X_{i} with rate parameters λ_{i} has a hypo-exponential distribution with rate vector (λ_{1}, …, λ_{n}).
The hypo-exponential distribution is a generalization of the Erlang distribution (a Gamma distribution with an integer-valued shape parameter) and a special case of the phase-type distribution (see References section).
The quantile function is computed by numeric inversion (using
uniroot
).
dhypoexp
gives the density, phypoexp
gives the distribution
function (or the integrated tail area distribution function),
qhypoexp
gives the quantile function, rhypoexp
generates
random deviates and mgfhypoexp
gives the moment-generating function
(or its derivative up to the second order).
If length(rate) == 1
, dhypoexp
, phypoexp
and
rhypoexp
are equivalent to dexp
,
pexp
and rexp
with rate parameter
rate
and should, in fact, be replaced by the latter ones for
computation speed.
Neuts, M. F. (1981) Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, reprinted and corrected.
1 2 3 4 5 6 7 8 9 10 11 | ## Random generation
rhypoexp(10, c(3, 5))
## Mean
mu <- mgfhypoexp(0, c(3, 5), difforder = 1)
## Variance
mgfhypoexp(0, c(3, 5), difforder = 2) - mu^2
## Quantile
qhypoexp(0.5, c(3, 5))
|
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