EXP {nsRFA} | 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 http://en.wikipedia.org/wiki/Exponential_distribution for a brief introduction on the Exponential distribution.
Definition
Parameters (2): ξ (lower endpoint of the distribution), α (scale).
Range of x: ξ ≤ x < ∞.
Probability density function:
f(x) = α^{-1} \exp\{-(x-ξ)/α\}
Cumulative distribution function:
F(x) = 1 - \exp\{-(x-ξ)/α\}
Quantile function:
x(F) = ξ - α \log(1-F)
L-moments
λ_1 = ξ + α
λ_2 = 1/2 \cdot α
τ_3 = 1/3
τ_4 = 1/6
Parameters
If ξ is known, α is given by α = λ_1 - ξ and the L-moment, moment, and maximum-likelihood estimators are identical. If ξ is unknown, the parameters are given by
α = 2 λ_2
ξ = λ_1 - α
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 (λ_1, λ_2, τ_3, τ_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)