Description Usage Arguments Value Examples

View source: R/Fuzzy_p_value_26102018.R

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
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
)
``` |

`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 |

`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. |

Returns the defuzzified p-value and the decision made.

1 2 3 4 | ```
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")
``` |

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