Entropy-based test for two SAR samples — entropy

Tests whether two samples come from the same distribution by comparing their estimated Shannon entropies. Under the null hypothesis of equal entropies, and by the asymptotic normality of the maximum likelihood estimator of the entropy, $$S = \frac{(\hat H_1 - \hat H_2)^2}{\widehat{\mathrm{Var}}(\hat H_1) + \widehat{\mathrm{Var}}(\hat H_2)}$$ follows asymptotically a $\chi^2_1$ distribution. This statistic is the basis of the entropy-based change detectors of the thesis of J. A. Ferreira (2021).

Usage

entropy_test(
  x,
  y,
  model = c("gamma", "g0i", "ggamma", "wishart", "g0p"),
  L = NULL
)

Arguments

x, y: Samples: numeric vectors of intensities (intensity models) or PolSAR observations (matrix models).
model: One of "gamma", "g0i", "ggamma", "wishart", "g0p".
L: Known number of looks; estimated when NULL.

Value

An object of class htest.

References

Ferreira, J. A. (2021). Entropias e somas compostas para matrizes estocásticas aplicadas a sistemas PolSAR. PhD thesis, Universidade Federal de Pernambuco.

Examples

set.seed(1)
x <- rg0i(200, alpha = -3, gamma = 2, L = 4)
y <- rg0i(200, alpha = -3, gamma = 2, L = 4)
z <- rg0i(200, alpha = -1.5, gamma = 1, L = 4)
entropy_test(x, y, model = "g0i", L = 4)
#> 
#> 	Shannon entropy test (G0I model)
#> 
#> data:  x and y
#> S = 2.989, df = 1, p-value = 0.08383
#> alternative hypothesis: true difference in entropies is not equal to 0
#> sample estimates:
#> entropy of x entropy of y 
#>    0.7837866    0.9918088 
#> 
entropy_test(x, z, model = "g0i", L = 4)$p.value
#> [1] 0.001877851