Gamma model for SAR intensities (R6)

R6 class for the multilook Gamma law $\Gamma(\mu, L)$; see dgammasar(). The maximum likelihood estimator of $\mu$ is the sample mean and $L$ solves $\log L - \psi^{(0)}(L) = \log\bar z - \overline{\log z}$.

Super class

SARModel -> GammaSAR

Methods

Public methods

GammaSAR$new()
GammaSAR$density()
GammaSAR$random()
GammaSAR$fit()
GammaSAR$entropy()
GammaSAR$entropy_variance()
GammaSAR$clone()

Inherited methods

`GammaSAR$new()`

Create a Gamma model.

Usage

GammaSAR$new(mu = 1, L = 1)

Arguments

mu: Mean.
L: Number of looks.

`GammaSAR$density()`

(Log-)density.

Usage

GammaSAR$density(x, log = FALSE)

Arguments

x: Numeric vector of intensities.
log: Return log-densities?

`GammaSAR$random()`

Simulate intensities.

Usage

GammaSAR$random(n)

Arguments

n: Number of observations.

`GammaSAR$fit()`

Fit by maximum likelihood.

Usage

GammaSAR$fit(x, L = NULL)

Arguments

x: Numeric vector of positive intensities.
L: Known number of looks. If NULL (default) it is estimated.

`GammaSAR$entropy()`

Shannon entropy.

Usage

GammaSAR$entropy()

`GammaSAR$entropy_variance()`

Asymptotic variance of the entropy estimator (closed form).

Usage

GammaSAR$entropy_variance(n = self$n)

Arguments

n: Sample size.

`GammaSAR$clone()`

The objects of this class are cloneable with this method.

Usage

GammaSAR$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

set.seed(1)
z <- rgammasar(500, mu = 2, L = 4)
m <- GammaSAR$new()$fit(z)
m
#> <Gamma> fitted to n = 500 observations
#>   mu = 1.97692
#>   L = 3.86696
#>   logLik = -666.161
#>   Shannon entropy = 1.33232
m$entropy()
#> [1] 1.332323
m$entropy_variance()
#> [1] 0.001113651
generics::tidy(m)
#> # A tibble: 2 × 4
#>   term  estimate std.error fixed
#>   <chr>    <dbl>     <dbl> <lgl>
#> 1 mu        1.98    0.0450 FALSE
#> 2 L         3.87    0.235  FALSE