pypfilt.stats¶
Note that there are 9 common definitions of sample quantiles.
Weighted versions of these 9 definitions are presented in
this article.
The qtl_wt()
function currently implements type 2 weighted quantiles.
However, the differences between these definitions is typically small when there are many values (i.e., particles).
- pypfilt.stats.cov_wt(x, wt, cor=False)¶
Estimate the weighted covariance or correlation matrix.
Equivalent to
cov.wt(x, wt, cor, center=TRUE, method="unbiased")
as provided by thestats
package for R.- Parameters
x – A 2-D array; columns represent variables and rows represent observations.
wt – A 1-D array of observation weights.
cor – Whether to return a correlation matrix instead of a covariance matrix.
- Returns
The covariance matrix (if
cor=False
) or the correlation matrix (ifcor=True
).
- pypfilt.stats.avg_var_wt(x, weights, biased=True)¶
Return the weighted average and variance (based on a Stack Overflow answer).
- Parameters
x – A 1-D array of values.
weights – A 1-D array of normalised weights.
biased – Use a biased variance estimator.
- Returns
A tuple that contains the weighted average and weighted variance.
- Raises
ValueError – if
x
orweights
are not one-dimensional, or ifx
andweights
have different dimensions.
- pypfilt.stats.qtl_wt(x, weights, probs)¶
Calculate weighted quantiles of an array of values, where each value has a fractional weighting.
Weights are summed over exact ties, yielding distinct values x_1 < x_2 < … < x_N, with corresponding weights w_1, w_2, …, w_N. Let
s_j
denote the sum of the first j weights, and letW
denote the sum of all the weights. For a probabilityp
:If
p * W < s_1
the estimated quantile isx_1
.If
s_j < p * W < s_{j + 1}
the estimated quantile isx_{j + 1}
.If
p * W == s_N
the estimated quantile isx_N
.If
p * W == s_j
the estimated quantile is(x_j + x_{j + 1}) / 2
.
- Parameters
x – A 1-D array of values.
weights – A 1-D array of weights.
probs – The quantile(s) to compute.
- Returns
The array of weighted quantiles.
- Raises
ValueError – if
x
orweights
are not one-dimensional, or ifx
andweights
have different dimensions.
- pypfilt.stats.cred_wt(x, weights, creds)¶
Calculate weighted credible intervals.
- Parameters
x – A 1-D array of values.
weights – A 1-D array of weights.
creds (List(int)) – The credible interval(s) to compute (
0..100
, where0
represents the median and100
the entire range).
- Returns
A dictionary that maps credible intervals to the lower and upper interval bounds.
- Raises
ValueError – if
x
orweights
are not one-dimensional, or ifx
andweights
have different dimensions.