Description Usage Arguments Details Value
exp_family
objects contain all required information in an exponential family to perform the E-step. The exponential function is encoded by
h(p; η) = exp{(η(μ) - η(μ*)) g(p) - (A(μ) - A(μ*))}
where g(p) is an arbitrary transformation, μ is the mean parameter, η is the natural parameter, and A(μ) is the partition function. The extra redundant parameter μ* is to guarantee that U([0, 1]) belongs to the class.
1 2 3 4 5 | gen_exp_family(g, ginv, eta, mustar, A, name = NULL, family = NULL)
beta_family()
inv_gaussian_family()
|
g |
a function. An transformation of p-values |
ginv |
a function. The inverse function of |
eta |
a function. The natural parameter as a function of the mean parameter |
mustar |
a scalar. The mean parameter that gives U([0, 1]) |
A |
a function. The partition function |
name |
a string. A name for the family. NULL by default |
family |
an object of class " |
Beta family (beta_family()
): modeling p-values as Beta-distributed random variables, i.e. g(p) = -log(p), η(μ) = -1 / μ, μ* = 1, A(μ) = log(μ), name = "beta" and family = Gamma(). Beta-family is highly recommended for general problems and used as default.
Inverse-gaussian family (inv_gaussian_family()
): modeling p-values as transformed z-scores, i.e. g(p) = Φ^{-1}(p) (Φ is the c.d.f. of a standard normal random variable), η(μ) = μ, μ* = 0, A(μ) = μ^2 / 2, name = "inv_gaussian" and family = gaussian().
an object of class "exp_family". This includes all inputs and h
, the density function.
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