[oneMath][stats] Add formulae to statistic routines

source/elements/oneMath/source/domains/stats/onemath_stats_central_moment.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::central_moment function is used to compute an array of
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of central moments:
+
+:math:`C^k(X) = \left( C^k_1(X), \; \dots, C^k_p(X) \right), \; C_i^k(X) =  \frac{1}{W} \sum_{j=1}^{n} \omega_j \left( x_{ij} - M_i(X) \right)^k`
+
+Where:
+
+:math:`W = \sum_{j=1}^n \omega_j, \, i = 1, \dots, p, \; k = 2, 3, 4`
+
+
 .. _onemath_stats_central_moment_buffer:
 
 central_moment (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_central_moment_user_mean.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::central_moment function is used to compute an array of
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of central moments:
+
+:math:`C^k(X) = \left( C^k_1(X), \; \dots, C^k_p(X) \right), \; C_i^k(X) =  \frac{1}{W} \sum_{j=1}^{n} \omega_j \left( x_{ij} - M_i(X) \right)^k`
+
+Where:
+
+:math:`W = \sum_{j=1}^n \omega_j, \, i = 1, \dots, p, \; k = 2, 3, 4`
+
+
 .. _onemath_stats_central_moment_user_mean_buffer:
 
 central_moment with provided mean (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_central_sum.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::central_sum function is used to compute an array of cen
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of central sums:
+
+:math:`S^k(X) = \left( S^k_1(X), \; \dots, S^k_p(X) \right), \; S^k_i(X) = \sum_{j=1}^{n} \omega_j \left( x_{ij} - S_i(X) \right)^k`
+
+Where:
+
+:math:`S_i(X) = \sum_{j=1}^n \omega_j x_{ij}, \; i = 1, \dots, p, \; k = 2, 3, 4`
+
+
 .. _onemath_stats_central_sum_buffer:
 
 central_sum (Buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_central_sum_user_mean.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::central_sum function is used to compute an array of cen
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of central sums:
+
+:math:`S^k(X) = \left( S^k_1(X), \; \dots, S^k_p(X) \right), \; S^k_i(X) = \sum_{j=1}^{n} \omega_j \left( x_{ij} - S_i(X) \right)^k`
+
+Where:
+
+:math:`S_i(X) = \sum_{j=1}^n \omega_j x_{ij}, \; i = 1, \dots, p, \; k = 2, 3, 4`
+
+
 .. _onemath_stats_central_sum_user_mean_buffer:
 
 central_sum with provided mean (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::kurtosis function is used to compute a kurtosis array (
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of kurtosis values:
+
+:math:`B(X) = \left( B_1(X), \; \dots, B_p(X) \right), \; B_i(X) = \frac{C^{(4)}_i(X)}{V^2_i(X)} - 3`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_kurtosis_buffer:
 
 kurtosis (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis_user_mean.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::kurtosis function is used to compute an array of kurtos
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of kurtosis values:
+
+:math:`B(X) = \left( B_1(X), \; \dots, B_p(X) \right), \; B_i(X) = \frac{C^{(4)}_i(X)}{V^2_i(X)} - 3`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_kurtosis_user_mean_buffer:
 
 kurtosis with provided mean (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_max.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::max function is used to compute a max values arrays (ma
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of maximum values:
+
+:math:`\max(X) = \left( {\max}_1(X), \; \dots, {\max}_p(X) \right)`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_max_buffer:
 
 max (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_mean.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::mean function is used to compute a mean array (mean val
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of mean values:
+
+:math:`M(X) = \left( M_1(X), \; \dots, M_p(X) \right), \; M_i(X) = \frac{1}{W} \sum_{j=1}^n \omega_j x_{ij}`
+
+Where:
+
+:math:`W = \sum_{j=1}^n \omega_j, \; i = 1, \dots, p`
+
+
 .. _onemath_stats_mean_buffer:
 
 mean (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_min.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::min function is used to compute min arrays (min value f
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of minimum values:
+
+:math:`\min(X) = \left( {\min}_1(X), \; \dots, {\min}_p(X) \right)`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_min_buffer:
 
 min (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_min_max.rst

@@ -25,6 +25,21 @@ The oneapi::math::stats::min_max function is used to compute min and max arrays
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of maximum values:
+
+:math:`\max(X) = \left( {\max}_1(X), \; \dots, {\max}_p(X) \right)`
+
+Vector of minimum values:
+
+:math:`\min(X) = \left( {\min}_1(X), \; \dots, {\min}_p(X) \right)`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_min_max_buffer:
 
 min_max (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_raw_moment.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::raw_moment function is used to compute array of raw mom
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of raw moments values:
+
+:math:`R^k(X) = \left( R^k_1(X), \; \dots, R^k_p(X) \right), \; R^k_i(X) = \frac{1}W \sum_{j=1}^n \omega_j x_{ij}^k`
+
+Where:
+
+:math:`W = \sum_{j=1}^n \omega_j, \; j = 1, \dots, p; k = 1, 2, 3, 4`
+
+
 .. _onemath_stats_raw_moment_buffer:
 
 oneapi::math::stats::raw_moment (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_raw_sum.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::raw_sum function is used to compute an array of raw sum
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of raw sums:
+
+:math:`S^k(X) = \left( S^k_1(X), \; \dots, S^k_p(X) \right), \; S_i^k(X) = \sum_{j=1}^n \omega_j x^k_{ij}`
+
+Where:
+
+:math:`i = 1, \dots, p, \; k = 1, 2, 3, 4`
+
+
 .. _onemath_stats_raw_sum_buffer:
 
 raw_sum (Buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_skewness.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::skewness function is used to compute a skewness array (
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of skewness values:
+
+:math:`\Gamma(X) = \left( \Gamma_1(X), \; \dots, \Gamma_p(X) \right), \; \Gamma_i(X) = \frac{C^{(3)}_i(X)}{V^{1.5}_i(X)}`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_skewness_buffer:
 
 skewness (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_skewness_user_mean.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::skewness function is used to compute an array of skewne
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of skewness values:
+
+:math:`\Gamma(X) = \left( \Gamma_1(X), \; \dots, \Gamma_p(X) \right), \; \Gamma_i(X) = \frac{C^{(3)}_i(X)}{V^{1.5}_i(X)}`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_skewness_user_mean_buffer:
 
 skewness with provided mean (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_variation.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::variation function is used to compute a variation array
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of variation coefficients:
+
+:math:`VC(X) = \left( VC_1(X), \; \dots, VC_p(X) \right), \; VC_i(X) = \frac{V^{0.5}_i(X)}{M_i(X)}`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_variation_buffer:
 
 variation (buffer version)

source/elements/oneMath/source/domains/stats/onemath_stats_variation_user_mean.rst

@@ -25,6 +25,17 @@ The oneapi::math::stats::variation function is used to compute an array of varia
         * - ``double``
 
 
+.. rubric:: Mathematical Notation
+
+Vector of variation coefficients:
+
+:math:`VC(X) = \left( VC_1(X), \; \dots, VC_p(X) \right), \; VC_i(X) = \frac{V^{0.5}_i(X)}{M_i(X)}`
+
+Where:
+
+:math:`i = 1, \dots, p`
+
+
 .. _onemath_stats_variation_user_mean_buffer:
 
 oneapi::math::stats::variation (buffer version)