diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_central_moment.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_central_moment.rst index 4a88ec7c2c..5bc39e19b2 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_central_moment.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_central_moment_user_mean.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_central_moment_user_mean.rst index 7288feda4a..7b6eaabf5f 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_central_moment_user_mean.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_central_sum.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_central_sum.rst index ccce90f454..6daf243a25 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_central_sum.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_central_sum_user_mean.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_central_sum_user_mean.rst index 14b67f9af4..d189d94ad9 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_central_sum_user_mean.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis.rst index 3551c3c678..d60787fa8f 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis_user_mean.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis_user_mean.rst index 6d70aeb6b1..f5646807f7 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_kurtosis_user_mean.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_max.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_max.rst index 48e3e88e66..bf3515ecb5 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_max.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_mean.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_mean.rst index 993f06175d..059272685e 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_mean.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_min.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_min.rst index 93c90d4ce8..8b03c55bb8 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_min.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_min_max.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_min_max.rst index 23440e16db..d33313cfb2 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_min_max.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_raw_moment.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_raw_moment.rst index 3414fbbdad..94fbe23aac 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_raw_moment.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_raw_sum.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_raw_sum.rst index dffe1ddf46..a30008185a 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_raw_sum.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_skewness.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_skewness.rst index 7a03202da4..9048e48e54 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_skewness.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_skewness_user_mean.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_skewness_user_mean.rst index 94570e4df8..95d05b3e42 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_skewness_user_mean.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_variation.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_variation.rst index 61b2d6b146..685f8122ac 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_variation.rst +++ b/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) diff --git a/source/elements/oneMath/source/domains/stats/onemath_stats_variation_user_mean.rst b/source/elements/oneMath/source/domains/stats/onemath_stats_variation_user_mean.rst index eb424e0a6e..586a741bf8 100755 --- a/source/elements/oneMath/source/domains/stats/onemath_stats_variation_user_mean.rst +++ b/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)