Kurtosis {FuzzySTs}

Calculates the excess of kurtosis of a random fuzzy variable

Description

Calculates the excess of kurtosis of a random fuzzy variable

Usage

Kurtosis(
  data.fuzzified,
  dist.type,
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100
)

Arguments

data.fuzzified

a fuzzification matrix constructed by a call to the function FUZZ or the function GFUZZ, or a similar matrix. No NA are allowed.

dist.type

type of distance chosen from the family of distances. The different choices are given by: "Rho1", "Rho2", "Bertoluzza", "Rhop", "Delta.pq", "Mid/Spr", "wabl", "DSGD", "DSGD.G", "GSGD".

i

parameter of the density function of the Beta distribution, fixed by default to i = 1.

j

parameter of the density function of the Beta distribution, fixed by default to j = 1.

theta

a numerical value between 0 and 1, representing a weighting parameter. By default, theta is fixed to 1/3 referring to the Lebesgue space. This measure is used in the calculations of the following distances: d_Bertoluzza, d_mid/spr and d_phi-wabl/ldev/rdev.

thetas

a decimal value between 0 and 1, representing the weight given to the shape of the fuzzy number. By default, thetas is fixed to 1. This parameter is used in the calculations of the d_theta star and the d_GSGD distances.

p

a positive integer such that 1 \le p < infinity, referring to the parameter of the Rho_p and Delta_pq. By default, p is fixed to 2.

q

a decimal value between 0 and 1, referring to the parameter of the metric Delta_pq. By default, q is fixed to 0.5.

breakpoints

a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.

Value

A numerical value.

Examples

mat <- matrix(c(1,2,0.25,1.8,2,2.6,0.5,3,3,2.6,3.8,4,4,4.2,3.9,5), ncol =4)
Kurtosis(mat, dist.type = "GSGD")