Exponential fitting

Generic functions to fit exponential populations.

These functions can be used directly, or, in a typical FRETBursts workflow they are passed to higher level methods.

See also:

fretbursts.fit.exp_fitting.expon_fit(s, s_min=0, offset=0.5, calc_residuals=True)

Fit sample s to an exponential distribution using the ML estimator.

This function computes the rate (Lambda) using the maximum likelihood (ML) estimator of the mean waiting-time (Tau), that for an exponentially distributed sample is the sample-mean.

Parameters:
  • s (array) – array of exponetially-distributed samples
  • s_min (float) – all samples < s_min are discarded (s_min must be >= 0).
  • offset (float) – offset for computing the CDF. See get_ecdf().
  • calc_residuals (bool) – if True compute the residuals of the fitted exponential versus the empirical CDF.
Returns:

A 4-tuple of the fitted rate (1/life-time), residuals array, residuals x-axis array, sample size after threshold.
fretbursts.fit.exp_fitting.expon_fit_cdf(s, s_min=0, offset=0.5, calc_residuals=True)

Fit of an exponential model to the empirical CDF of s.

This function computes the rate (Lambda) fitting a line (linear regression) to the log of the empirical CDF.

Parameters:
  • s (array) – array of exponetially-distributed samples
  • s_min (float) – all samples < s_min are discarded (s_min must be >= 0).
  • offset (float) – offset for computing the CDF. See get_ecdf().
  • calc_residuals (bool) – if True compute the residuals of the fitted exponential versus the empirical CDF.
Returns:

A 4-tuple of the fitted rate (1/life-time), residuals array, residuals x-axis array, sample size after threshold.
fretbursts.fit.exp_fitting.expon_fit_hist(s, bins, s_min=0, weights=None, offset=0.5, calc_residuals=True)

Fit of an exponential model to the histogram of s using least squares.

Parameters:
  • s (array) – array of exponetially-distributed samples
  • bins (float or array) – if float is the bin width, otherwise is the array of bin edges (passed to numpy.histogram)
  • s_min (float) – all samples < s_min are discarded (s_min must be >= 0).
  • weights (None or string) – if None no weights is applied. if is ‘hist_counts’, each bin has a weight equal to its counts if is ‘inv_hist_counts’, the weight is the inverse of the counts.
  • offset (float) – offset for computing the CDF. See get_ecdf().
  • calc_residuals (bool) – if True compute the residuals of the fitted exponential versus the empirical CDF.
Returns:

A 4-tuple of the fitted rate (1/life-time), residuals array, residuals x-axis array, sample size after threshold.
fretbursts.fit.exp_fitting.get_ecdf(s, offset=0.5)

Return arrays (x, y) for the empirical CDF curve of sample s.

See the code for more info (is a one-liner!).

Parameters:
  • s (array of floats) – sample
  • offset (float, default 0.5) – Offset to add to the y values of the CDF
Returns:

(x, y) (tuple of arrays) – the x and y values of the empirical CDF
fretbursts.fit.exp_fitting.get_residuals(s, tau_fit, offset=0.5)

Returns residuals of sample s CDF vs an exponential CDF.

Parameters:
  • s (array of floats) – sample
  • tau_fit (float) – mean waiting-time of the exponential distribution to use as reference
  • offset (float) – Default 0.5. Offset to add to the empirical CDF. See get_ecdf() for details.
Returns:

residuals (array) – residuals of empirical CDF compared with analytical CDF with time constant tau_fit.