fgamma: ML estimation of the Gamma distribution

In Renext: Renewal Method for Extreme Values Extrapolation

ML estimation of the Gamma distribution

Description

Fast Maximum Likelihood estimation of the Gamma distribution.

Usage

fgamma(x, check.loglik = FALSE)

Arguments

x	Sample vector to be fitted. Should contain only positive non-NA values.
check.loglik	If TRUE, the log-likelihood is recomputed using dgamma function with log = TRUE. The result is returned as a list element.

Details

The likelihood is concentrated with respect to the scale parameter. The concentrated log-likelihood is a strictly concave function of the shape parameter which can easily maximised numerically.

Value

A list with the following elements

estimate	Parameter ML estimates.
sd	Vector of (asymptotic) standard deviations for the estimates.
loglik	The maximised log-likelihood.
check.loglik	The checked log-likelihood.
cov	The (asymptotic) covariance matrix computed from theoretical or observed information matrix.
info	The information matrix.

Note

The distribution is fitted by using the scale parameter rather than rate (inverse of scale).

Author(s)

Yves Deville

See Also

GammaDist in the stats package.

Examples

set.seed(9876)
alpha <- 0.06
beta <- rexp(1)
n <- 30
x <- rgamma(n, shape = alpha, scale = beta)
fit <- fgamma(x, check.loglik = TRUE)

## compare with MASS results
if (require(MASS)) {
   fit.MASS <- fitdistr(x, densfun = "gamma")
   rate <- 1 / fit$estimate["scale"]
   est <- c(fit$estimate, rate = rate)
   der <- rate * rate ## derivative of rate w.r.t scale
   sdest <- c(fit$sd, rate = der * fit$sd["scale"])
   tab <- rbind(sprintf(" %10.8f ", est),
                sprintf("(%10.8f)", sdest))
   colnames(tab) <- c("shape", "scale", "rate")
   rownames(tab) <- c("est", "sd")
   noquote(tab)
}

Renext documentation built on Aug. 30, 2023, 1:06 a.m.