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.