Construct a BDEGP-Family

Constructs a BDEGP-Family distribution with fixed number of components and blending interval.

Usage

dist_bdegp(n, m, u, epsilon)

Arguments

n

Number of dirac components, starting with a point mass at 0.

m

Number of erlang components, translated by n - 0.5.

u

Blending cut-off, must be a positive real.

epsilon

Blending radius, must be a positive real less than u. The blending interval will be u - epsilon < x < u + epsilon.

Value

• A MixtureDistribution of

  • n DiracDistributions at 0 .. n - 1 and

  • a BlendedDistribution object with child Distributions

    • a TranslatedDistribution with offset n - 0.5 of an ErlangMixtureDistribution with m shapes

    • and a GeneralizedParetoDistribution with shape parameter restricted to [0, 1] and location parameter fixed at u With break u and bandwidth epsilon.

See also

Other Distributions: Distribution, dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

dist <- dist_bdegp(n = 1, m = 2, u = 10, epsilon = 3)
params <- list(
  dists = list(
    list(),
    list(
      dists = list(
        list(
          dist = list(
            shapes = list(1L, 2L),
            scale = 1.0,
            probs = list(0.7, 0.3)
          )
        ),
        list(
          sigmau = 1.0,
          xi = 0.1
        )
      ),
      probs = list(0.1, 0.9)
    )
  ),
  probs = list(0.95, 0.05)
)
x <- dist$sample(100, with_params = params)

plot_distributions(
  theoretical = dist,
  empirical = dist_empirical(x),
  .x = seq(0, 20, length.out = 101),
  with_params = list(theoretical = params)
)
#> Warning: Removed 33 rows containing missing values or values outside the scale range
#> (`geom_line()`).