EXP | R Documentation |
EXP
provides the link between L-moments of a sample and the two parameter
exponential distribution.
f.exp (x, xi, alfa)
F.exp (x, xi, alfa)
invF.exp (F, xi, alfa)
Lmom.exp (xi, alfa)
par.exp (lambda1, lambda2)
rand.exp (numerosita, xi, alfa)
x |
vector of quantiles |
xi |
vector of exp location parameters |
alfa |
vector of exp scale parameters |
F |
vector of probabilities |
lambda1 |
vector of sample means |
lambda2 |
vector of L-variances |
numerosita |
numeric value indicating the length of the vector to be generated |
See https://en.wikipedia.org/wiki/Exponential_distribution for a brief introduction on the Exponential distribution.
Definition
Parameters (2): \xi
(lower endpoint of the distribution), \alpha
(scale).
Range of x
: \xi \le x < \infty
.
Probability density function:
f(x) = \alpha^{-1} \exp\{-(x-\xi)/\alpha\}
Cumulative distribution function:
F(x) = 1 - \exp\{-(x-\xi)/\alpha\}
Quantile function:
x(F) = \xi - \alpha \log(1-F)
L-moments
\lambda_1 = \xi + \alpha
\lambda_2 = 1/2 \cdot \alpha
\tau_3 = 1/3
\tau_4 = 1/6
Parameters
If \xi
is known, \alpha
is given by \alpha = \lambda_1 - \xi
and the L-moment, moment, and maximum-likelihood estimators are identical.
If \xi
is unknown, the parameters are given by
\alpha = 2 \lambda_2
\xi = \lambda_1 - \alpha
For estimation based on a single sample these estimates are inefficient, but in regional frequency analysis they can give reasonable estimates of upper-tail quantiles.
Lmom.exp
and par.exp
accept input as vectors of equal length. In f.exp
, F.exp
, invF.exp
and rand.exp
parameters (xi
, alfa
) must be atomic.
f.exp
gives the density f
, F.exp
gives the distribution function F
, invFexp
gives
the quantile function x
, Lmom.exp
gives the L-moments (\lambda_1
, \lambda_2
, \tau_3
, \tau_4
), par.exp
gives the parameters (xi
, alfa
), and rand.exp
generates random deviates.
For information on the package and the Author, and for all the references, see nsRFA
.
rnorm
, runif
, GENLOGIS
, GENPAR
, GEV
, GUMBEL
, KAPPA
, LOGNORM
, P3
; DISTPLOTS
, GOFmontecarlo
, Lmoments
.
data(hydroSIMN)
annualflows
summary(annualflows)
x <- annualflows["dato"][,]
fac <- factor(annualflows["cod"][,])
split(x,fac)
camp <- split(x,fac)$"45"
ll <- Lmoments(camp)
parameters <- par.exp(ll[1],ll[2])
f.exp(1800,parameters$xi,parameters$alfa)
F.exp(1800,parameters$xi,parameters$alfa)
invF.exp(0.7870856,parameters$xi,parameters$alfa)
Lmom.exp(parameters$xi,parameters$alfa)
rand.exp(100,parameters$xi,parameters$alfa)
Rll <- regionalLmoments(x,fac); Rll
parameters <- par.exp(Rll[1],Rll[2])
Lmom.exp(parameters$xi,parameters$alfa)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.