Compute the average lifetime by integrating the correlation function as a function of lead time. When not using the 1/e rule, the correlation function must be long enough to converge to 0, otherwise the lifetime is underestimated. The correlation function can be either empirical or theoretical, e.g. derived using the function ‘ar_acf’ in timeseries/autoregression.py.

Parameters
• X_s (array-like) – Array with the correlation function. Works also with other decaying scores that are defined in the range [0,1]=[min_skill,max_skill].

• X_t (array-like) – Array with the forecast lead times in the desired unit, e.g. [min, hour].

• rule (str {'1/e', 'trapz', 'simpson'}, optional) –

Name of the method to integrate the correlation curve.

’1/e’ uses the 1/e rule and assumes an exponential decay. It linearly interpolates the time when the correlation goes below the value 1/e. When all values are > 1/e it returns the max lead time. When all values are < 1/e it returns the min lead time.

’trapz’ uses the trapezoidal rule for integration.

’simpson’ uses the Simpson’s rule for integration.

Returns

lf – Estimated lifetime with same units of X_t.

Return type

float