Module pydsphtools.stats

A module with basic statistics functions.

Functions

def agreement_idx(obs: Sequence[float], pred: Sequence[float], c: float = 2) ‑> float

Calulcates the index of agreement (dr) following the paper by Willmott et al.[1].

Parameters

obs : numpy array-like

The observed values as an array-like object

pred : numpy array-like

The predicted values as an array-like object

c : float, optional

The scaling factor. By default 2

Returns

float

The value of the index of agreement

References

[1] Cort J. Willmott, Scott M. Robeson, and Kenji Matsuura, "A refined index of model performance", International Journal of Climatology, Volume 32, Issue 13, pages 2088-2094, 15 November 2012, https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.2419.

def bias(y: Sequence[float], obs: Sequence[float], normalize: bool = False) ‑> float

Calculates Root Mean Square Error between two signals.

Parameters

y : array-like

The prediction signal.

obs : array-like

The observation signal.

normalize : bool

If True the output will be the bias is normilized using the obs array. By default, False.

Returns

float

The bias between the two signals.

Notes

The bias is calculated using the following formula:

$$BIAS = \frac{1}{N} \sum^N_{i=1} (y_i - y_{obs})$$

def l1_norm(signal1: Sequence[float], signal2: Sequence[float], x: Optional[Sequence[float]] = None, dx: float = 1.0) ‑> float

Calculates the L¹-norm between signal. See Notes for more details.

Parameters

signal1 : array-like

The first signal.

signal2 : array-like

The second signal

x : array-like, optional

The sample points corresponding to the y values. If x is None, the sample points are assumed to be evenly spaced dx apart. Default, None.

dx : scalar, optional

The spacing between sample points when x is None. Default, 1.

Returns

float

The L¹-norm of the two signals.

Notes

The L¹-norm is calculated using the following formula:

$$L^1 \text{-norm} = \int_{x_0}^{x_f} \left| f_1(x) - f_2(x) \right| dx$$

where $f_1(x)$ is signal1 and $f_2(x)$ is signal2.

def rmse(y: Sequence[float], obs: Sequence[float]) ‑> float

Calculates Root Mean Square Error between two signals.

Parameters

y : array-like

The prediction signal.

obs : array-like

The observation signal.

Returns

float

The RMSE between the two signals.

Notes

The RMSE is calculated using the following formula:

$$RMSE = \sqrt{\frac{\sum^N_{i=1} (y_i - y_{obs})^2}{N}}$$