# Box Cox transformation¶

the estimation of the Box Cox transformation from a given field of the process ,

the action of the Box Cox transformation on a field generated from .

**Marginal Box Cox transformation:**

which leads to:

and then:

To have constant with respect to at the first order, we need:

(1)¶

Now, we make some additional hypotheses on the relation between and :

If we suppose that , then (1) leads to the function and we take ;

If we suppose that , then (1) leads to the function and we take ;

More generally, if we suppose that , then (1) leads to the function parametrized by the scalar :

(2)¶

where .

The inverse Box Cox transformation is defined by:

(3)¶

**Estimation of the Box Cox transformation:**

(4)¶

from which we derive the density probability function of for all vertices :

(5)¶

Using (5), the likelihood of the values with respect to the model (4) writes:

(6)¶

We notice that for each fixed , the likelihood equation is proportional to the likelihood equation which estimates . Thus, the maximum likelihood estimator for for a given are:

(7)¶

(8)¶

where is a constant.

The parameter is the one maximizing defined in (8).

API:

See

`BoxCoxTransform`

See

`BoxCoxFactory`

Examples: