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
.