Fuzzy.p.value {FuzzySTs}

Computes the fuzzy p-value of a given fuzzy hypothesis test

Description

Computes the fuzzy p-value of a given fuzzy hypothesis test

Usage

Fuzzy.p.value(
  type,
  H0,
  H1,
  t,
  s.d = 1,
  n,
  sig,
  distribution,
  distance.type = "DSGD",
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100
)

Arguments

type

a category betwenn "0", "1" and "2". The category "0" refers to a bilateral test, the category "1" for a lower unilateral one, and "2" for an upper unilateral test.

H0

a trapezoidal or a triangular fuzzy number representing the fuzzy null hypothesis.

H1

a trapezoidal or a triangular fuzzy number representing the fuzzy alternative hypothesis.

t

a given numerical or fuzzy type parameter of the distribution.

s.d

a numerical value for the standard deviation of the distribution.

n

the total number of observations of the data set.

sig

a numerical value representing the significance level of the test.

distribution

a distribution chosen between "normal", "poisson", "Student" or "Logistic".

distance.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, p 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

Returns the defuzzified p-value and the decision made.

Examples

H0 <- TriangularFuzzyNumber(2.2,2.5,3) 
H1 <- TriangularFuzzyNumber(2.5,2.5,5)
Fuzzy.p.value(type=1, H0, H1, t=TriangularFuzzyNumber(0.8,1.8,2.8),
s.d=0.7888, n=10, sig=0.05, distribution="normal", distance.type="GSGD")