define tensors

is the natural parameter vector

is the expectation parameter vector

is the third derivative of the potential function φ(η) at the origin η=0.

is the fourth derivative of the potential function φ(η) at the origin η=0.

is the third derivative of the cumulant function ψ(θ) at the origin θ=0.

is the fourth derivative of the cumulant function ψ(θ) at the origin θ=0.

is the random variable

is the first derivative of at the origin .

is the second derivative of at the origin .

is the inverse matrix of .

is the third derivative of at the origin .

is the fourth derivative of at the origin .