fstats_descriptive_statistics Module

private pure function covariance_array(x, y) result(rst)

Computes the sample covariance of two data sets.

The covariance computed is the sample covariance such that $$q_{jk} = \frac{\Sigma \left( x_{i} - \bar{x} \right) \left( y_{i} - \bar{y} \right)}{n - 1}$$ .

Arguments

Return Value real(kind=real64)

Sample covariance; fewer than two observations or nonfinite inputs give NaN. An unrepresentable result gives signed infinity.

private pure function covariance_columns(x, y) result(rst)

Computes sample covariance using independent copies of two columns. Unequal counts cause ERROR STOP with FS_ARRAY_SIZE_ERROR.

Arguments

Return Value real(kind=real64)

Sample covariance; fewer than two pairs or nonfinite values give NaN. Unrepresentable results give signed infinity.

private pure function covariance_column_array(x, y) result(rst)

Computes sample covariance between a column and an array, copying the column. Unequal counts cause ERROR STOP with FS_ARRAY_SIZE_ERROR.

Arguments

Return Value real(kind=real64)

Sample covariance; undersized/nonfinite data give NaN; unrepresentable results give signed infinity.

private pure function covariance_array_column(x, y) result(rst)

Computes sample covariance between an array and a column, copying the column. Unequal counts cause ERROR STOP with FS_ARRAY_SIZE_ERROR.

Arguments

Return Value real(kind=real64)

Sample covariance; undersized/nonfinite data give NaN; unrepresentable results give signed infinity.

private pure function mean_array(x) result(rst)

Computes the mean using a scaled, compensated sum.

Arguments

Return Value real(kind=real64)

Mean; empty arrays or nonfinite observations give NaN.

private pure function mean_column(x) result(rst)

Computes a column mean using a scaled, compensated sum without copying data.

Arguments

Return Value real(kind=real64)

Mean; empty arrays or nonfinite observations give NaN.

private pure function median_array(x) result(rst)

Computes the median of the values in an array.

Arguments

Return Value real(kind=real64)

Median; empty arrays or nonfinite observations give NaN.

private pure function median_column(x) result(rst)

Computes the median by sorting a copy, leaving the column unchanged.

Arguments

Return Value real(kind=real64)

Median; empty or nonfinite data give NaN.

private pure function pooled_variance_1(si, ni) result(rst)

Computes the pooled estimate of variance.

Arguments

Return Value real(kind=real64)

Pooled variance; empty inputs, nonfinite/negative variances, or groups with fewer than two observations give NaN.

private pure function pooled_variance_2(x) result(rst)

Computes the pooled estimate of variance.

Arguments

Return Value real(kind=real64)

Pooled variance; empty/unallocated groups or groups with fewer than two finite observations give NaN.

private pure function pooled_variance_column(si, ni) result(rst)

Pools variance estimates using the array implementation on a column copy. Unequal counts cause ERROR STOP with FS_ARRAY_SIZE_ERROR.

Arguments

Return Value real(kind=real64)

Pooled variance; empty data, negative/nonfinite estimates, or invalid group sizes give NaN.

private pure function pooled_variance_columns(x) result(rst)

Pools sample variances from an array of columns, copying each group's data.

Arguments

Return Value real(kind=real64)

Pooled variance; no groups, undersized/unallocated groups, or nonfinite observations give NaN, as in the array-container overload.

private pure function quantile_array(x, q) result(rst)

Computes the specified quantile of a data set using the SAS Method 4.

See Also

• Wikipedia

Arguments

Return Value real(kind=real64)

Quantile; empty/nonfinite data or q outside [0, 1] give NaN.

private pure function quantile_column(x, q) result(rst)

Computes a quantile using the array implementation on a copy.

Arguments

Return Value real(kind=real64)

Quantile; empty/nonfinite data or invalid/nonfinite q give NaN.

private pure function standard_deviation_array(x) result(rst)

Computes the sample standard deviation of the values in an array.

The value computed is the sample standard deviation. $$s = \sqrt{ \frac{\Sigma \left( x_{i} - \bar{x} \right)^2}{n - 1} }$$

Arguments

Return Value real(kind=real64)

Sample standard deviation; invalid/undersized data give NaN. It can remain finite even when the variance would overflow.

private pure function standard_deviation_column(x) result(rst)

Computes sample standard deviation using the array implementation on a copy.

Arguments

Return Value real(kind=real64)

Sample standard deviation; fewer than two values or nonfinite data give NaN. Unrepresentable results give positive infinity.

private function trimmed_mean_array(x, p) result(rst)

Computes the trimmed mean of a data set.

Arguments

Return Value real(kind=real64)

Trimmed mean; invalid p or empty/nonfinite data give NaN.

private function trimmed_mean_column(x, p) result(rst)

Computes the trimmed mean and sorts the column's values in ascending order. Uses a borrowed view without reallocating the underlying array.

Arguments

Return Value real(kind=real64)

Trimmed mean; empty/nonfinite data or invalid/nonfinite p give NaN.

private pure function variance_array(x) result(rst)

Computes the sample variance of the values in an array.

The variance computed is the sample variance such that $$s^2 = \frac{\Sigma \left( x_{i} - \bar{x} \right)^2}{n - 1}$$ .

Arguments

Return Value real(kind=real64)

Sample variance; fewer than two observations or nonfinite inputs give NaN. An unrepresentable variance gives positive infinity.

private pure function variance_column(x) result(rst)

Computes sample variance using the array implementation on a copy.

Arguments

Return Value real(kind=real64)

Sample variance; fewer than two values or nonfinite data give NaN. Unrepresentable results give positive infinity.