Calculate the nth centralized moment. Parameters ---------- a : Array Data over which to compute moment order : int Order of the moment that is returned, must be >= 2. axis : int, optional Axis along which the central moment is computed. The default is to
(
a, order, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None
)
| 558 | |
| 559 | |
| 560 | def moment( |
| 561 | a, order, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None |
| 562 | ): |
| 563 | """Calculate the nth centralized moment. |
| 564 | |
| 565 | Parameters |
| 566 | ---------- |
| 567 | a : Array |
| 568 | Data over which to compute moment |
| 569 | order : int |
| 570 | Order of the moment that is returned, must be >= 2. |
| 571 | axis : int, optional |
| 572 | Axis along which the central moment is computed. The default is to |
| 573 | compute the moment of the flattened array. |
| 574 | dtype : data-type, optional |
| 575 | Type to use in computing the moment. For arrays of integer type the |
| 576 | default is float64; for arrays of float types it is the same as the |
| 577 | array type. |
| 578 | keepdims : bool, optional |
| 579 | If this is set to True, the axes which are reduced are left in the |
| 580 | result as dimensions with size one. With this option, the result |
| 581 | will broadcast correctly against the original array. |
| 582 | ddof : int, optional |
| 583 | "Delta Degrees of Freedom": the divisor used in the calculation is |
| 584 | N - ddof, where N represents the number of elements. By default |
| 585 | ddof is zero. |
| 586 | |
| 587 | Returns |
| 588 | ------- |
| 589 | moment : Array |
| 590 | |
| 591 | References |
| 592 | ---------- |
| 593 | .. [1] Pebay, Philippe (2008), "Formulas for Robust, One-Pass Parallel |
| 594 | Computation of Covariances and Arbitrary-Order Statistical Moments", |
| 595 | Technical Report SAND2008-6212, Sandia National Laboratories. |
| 596 | |
| 597 | """ |
| 598 | if not isinstance(order, Integral) or order < 0: |
| 599 | raise ValueError("Order must be an integer >= 0") |
| 600 | |
| 601 | if order < 2: |
| 602 | reduced = a.sum(axis=axis) # get reduced shape and chunks |
| 603 | if order == 0: |
| 604 | # When order equals 0, the result is 1, by definition. |
| 605 | return ones( |
| 606 | reduced.shape, chunks=reduced.chunks, dtype="f8", meta=reduced._meta |
| 607 | ) |
| 608 | # By definition the first order about the mean is 0. |
| 609 | return zeros( |
| 610 | reduced.shape, chunks=reduced.chunks, dtype="f8", meta=reduced._meta |
| 611 | ) |
| 612 | |
| 613 | if dtype is not None: |
| 614 | dt = dtype |
| 615 | else: |
| 616 | dt = getattr(np.var(np.ones(shape=(1,), dtype=a.dtype)), "dtype", object) |
| 617 |