Descriptive statistics
- statinf.stats.descriptive.cov(x, y)[source]
Compute the covariance between two variables.
- Parameters
x (
numpy.array) – Input variable. Format can benumpy.array,listorpandas.Series.y (
numpy.array) – Input variable. Format can benumpy.array,listorpandas.Series.
- Formula
- \[Cov(\mathbf{X}, \mathbf{Y}) = \dfrac{ \sum_{i = 1}^{n} (X_{i} - \bar{X}) (Y_{i} - \bar{Y}) }{n - 1}\]
- Example
>>> from statinf import stats >>> x = [0.023699, 0.021436, 0.0200109, 0.0202762, 0.0165271, 0.01027] >>> y = [9.4228, 9.27951, 9.167963, 9.68820, 9.56490, 7.543] >>> stats.cov(x, y) ... 0.003047229298620001
- Reference
DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. Pearson Education.
- Returns
Covariance value.
- Return type
float
- statinf.stats.descriptive.pearson(x, y)[source]
Compute the Pearson’s coefficient correlation
- Parameters
x (
numpy.array) – Input variable. Format can benumpy.array,listorpandas.Series.y (
numpy.array) – Input variable. Format can benumpy.array,listorpandas.Series.
- Formula
- \[\rho = \dfrac{ Cov(X, Y) }{\sigma_{X} \sigma_{Y}}\]
where \(\sigma_{Z} = \sqrt{\mathbb{V}(Z)}\)
- Example
>>> from statinf import stats >>> x = [0.023699, 0.021436, 0.0200109, 0.0202762, 0.0165271, 0.01027] >>> y = [9.4228, 9.27951, 9.167963, 9.68820, 9.56490, 7.543] >>> stats.pearson(x, y) ... 0.9750052703452801
- Reference
DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. Pearson Education.
- Returns
Pearson’s coefficient correlation.
- Return type
float
- statinf.stats.descriptive.spearman(x, y)[source]
Spearman’s rank correlation coefficient.
- Parameters
x (
numpy.array) – Input variable. Format can benumpy.array,listorpandas.Series.y (
numpy.array) – Input variable. Format can benumpy.array,listorpandas.Series.
- Formula
- \[\rho = 1 - \dfrac{ 6 \sum_{i=1}^{n} d^{2} }{ n (n^{2} - 1)}\]
- Example
>>> from statinf import stats >>> x = [0.023699, 0.021436, 0.0200109, 0.0202762, 0.0165271, 0.01027] >>> y = [9.4228, 9.27951, 9.167963, 9.68820, 9.56490, 7.543] >>> stats.spearman(x, y) ... 0.37142857142857144
- Returns
Spearman’s rank correlation coefficient.
- Return type
float
- statinf.stats.descriptive.var(x, std=False, df=1)[source]
Compute the variance of a variable.
- Parameters
x (
numpy.array) – Input variable. Format can benumpy.array,listorpandas.Series.std (
bool, optional) – Returns standard deviation, i.e. \(\sqrt{\mathbb{V}(\mathbf{X})}\), defauls to False.df (
int, optional) – Degrees of freedom, defaults to 1.
- Formula
- \[\mathbb{V}(\mathbf{X}) = \dfrac{1}{n - 1} \sum_{i = 1}^{n} (X_{i} - \bar{X})^{2}\]
- Example
>>> from statinf import stats >>> x = [0.023699, 0.021436, 0.0200109, 0.0202762, 0.0165271, 0.01027] >>> stats.var(x) ... 2.2492979044000003e-05
- Returns
Variance.
- Return type
float