statsmodels.stats.multitest.NullDistribution

class statsmodels.stats.multitest.NullDistribution(zscores, null_lb=-1, null_ub=1, estimate_mean=True, estimate_scale=True, estimate_null_proportion=False)[source]

Estimate a Gaussian distribution for the null Z-scores.

The observed Z-scores consist of both null and non-null values. The fitted distribution of null Z-scores is Gaussian, but may have non-zero mean and/or non-unit scale.

Parameters:
  • zscores (array-like) – The observed Z-scores.
  • null_lb (float) – Z-scores between null_lb and null_ub are all considered to be true null hypotheses.
  • null_ub (float) – See null_lb.
  • estimate_mean (bool) – If True, estimate the mean of the distribution. If False, the mean is fixed at zero.
  • estimate_scale (bool) – If True, estimate the scale of the distribution. If False, the scale parameter is fixed at 1.
  • estimate_null_proportion (bool) – If True, estimate the proportion of true null hypotheses (i.e. the proportion of z-scores with expected value zero). If False, this parameter is fixed at 1.
mean

The estimated mean of the empirical null distribution

Type:float
sd

The estimated standard deviation of the empirical null distribution

Type:float
null_proportion

The estimated proportion of true null hypotheses among all hypotheses

Type:float

References

B Efron (2008). Microarrays, Empirical Bayes, and the Two-Groups Model. Statistical Science 23:1, 1-22.

Notes

See also:

http://nipy.org/nipy/labs/enn.html#nipy.algorithms.statistics.empirical_pvalue.NormalEmpiricalNull.fdr

Methods

pdf(zscores) Evaluates the fitted emirical null Z-score density.