tangent
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Search
Returned 99 matches (100 formulae, 64 docs)
Lookup 696.779 ms, Re-ranking 9809.170 ms
Found 813116 tuple postings, 162979 formulae, 20880 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
0.9046
0.9046
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dimensionless_quantity.html
∑
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Doc 2
0.5449
0.5449
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Correlation_and_dependence.html
r
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Doc 3
0.4989
0.4989
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Fisher_transformation.html
r
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Doc 4
0.4390
0.4390
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Assortativity.html
r
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Doc 5
0.4198
0.7847
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html
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Doc 6
0.4017
1.1461
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html
n
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Doc 7
0.3671
0.7275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html
b
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Doc 8
0.3546
0.3546
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Collaborative_filtering.html
simil
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Doc 9
0.3257
2.1012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
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Doc 10
0.3239
0.3239
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sufficient_statistic.html
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Doc 11
0.3135
0.5630
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hotelling's_T-squared_distribution.html
𝐖
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Doc 12
0.3063
0.6127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Conjugate_prior.html
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Doc 13
0.3046
0.8619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html
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Doc 14
0.2950
0.7884
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Multivariate_normal_distribution.html
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Doc 15
0.2884
0.4507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kurtosis.html
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Doc 16
0.2850
0.5243
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html
t
score
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Doc 17
0.2833
0.2833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Pivotal_quantity.html
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=
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¯
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Doc 18
0.2827
0.2827
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Reciprocity_(network_science).html
ρ
≡
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Doc 19
0.2793
0.5416
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Simple_linear_regression.html
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Doc 20
0.2765
0.2765
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Gravitational_lensing_formalism.html
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Doc 21
0.2751
0.2751
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Kuder–Richardson_Formula_20.html
σ
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Doc 22
0.2718
0.2718
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Regression_analysis.html
β
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Doc 23
0.2689
0.8776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html
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Doc 24
0.2662
0.3653
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html
σ
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i
-
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Doc 25
0.2619
0.2619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Linear_discriminant_analysis.html
Σ
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=
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(
μ
i
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Doc 26
0.2543
0.4328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html
s
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j
=
1
n
(
x
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j
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Doc 27
0.2523
0.4184
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Bias_of_an_estimator.html
∑
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=
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X
¯
)
2
1
n
∑
i
=
1
n
(
X
i
-
X
¯
)
2
<
1
n
∑
i
=
1
n
(
X
i
-
μ
)
2
,
Doc 28
0.2523
0.2523
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Partition_of_sums_of_squares.html
∑
i
=
1
n
(
y
i
-
y
¯
)
2
Doc 29
0.2448
0.2448
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Absolute_value.html
∑
i
=
1
n
(
a
i
-
b
i
)
2
.
Doc 30
0.2299
0.2299
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Covariance.html
q
j
k
=
1
N
-
1
∑
i
=
1
N
(
X
i
j
-
X
¯
j
)
(
X
i
k
-
X
¯
k
)
Doc 31
0.2154
0.2154
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Contrast_(vision).html
1
M
N
∑
i
=
0
N
-
1
∑
j
=
0
M
-
1
(
I
i
j
-
I
¯
)
2
,
Doc 32
0.2139
0.2139
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Errors-in-variables_models.html
β
^
=
1
T
∑
t
=
1
T
(
x
t
-
x
¯
)
(
y
t
-
y
¯
)
1
T
∑
t
=
1
T
(
x
t
-
x
¯
)
2
,
Doc 33
0.2117
0.2117
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Qualitative_variation.html
d
j
k
=
∑
i
=
1
N
(
x
i
j
-
x
i
k
)
2
Doc 34
0.2097
0.2097
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Well-behaved_statistic.html
s
M
=
∑
i
=
1
m
x
i
;
s
Σ
=
∑
i
=
1
m
(
x
i
-
x
¯
)
2
Doc 35
0.2081
0.2081
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/F-test.html
∑
i
j
(
Y
i
j
-
Y
¯
i
⋅
)
2
/
(
N
-
K
)
,
Doc 36
0.2058
0.2058
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Regression_toward_the_mean.html
β
^
=
∑
i
=
1
n
(
x
i
-
x
¯
)
(
y
i
-
y
¯
)
∑
i
=
1
n
(
x
i
-
x
¯
)
2
=
x
y
¯
-
x
¯
y
¯
x
2
¯
-
x
¯
2
=
Cov
[
x
,
y
]
Var
[
x
]
=
r
x
y
s
y
s
x
,
Doc 37
0.2008
0.3948
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cramér–Rao_bound.html
T
=
∑
i
=
1
n
(
X
i
-
μ
)
2
n
.
T
=
∑
i
=
1
n
(
X
i
-
μ
)
2
n
+
2
.
Doc 38
0.1992
0.1992
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Probability_theory.html
Z
n
=
∑
i
=
1
n
(
X
i
-
μ
)
σ
n
Doc 39
0.1935
0.2987
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Mean_square_weighted_deviation.html
σ
2
=
∑
i
=
1
N
w
i
(
x
i
-
x
¯
*
)
2
∑
i
=
1
N
w
i
s
2
=
∑
i
=
1
N
w
i
(
∑
i
=
1
N
w
i
)
2
-
∑
i
=
1
N
w
i
2
.
∑
i
=
1
N
w
i
(
x
i
-
x
¯
*
)
2
Doc 40
0.1911
0.1911
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Experimental_uncertainty_analysis.html
σ
^
i
=
∑
k
=
1
n
(
x
k
-
x
¯
i
)
2
n
-
1
σ
^
i
,
j
=
∑
k
=
1
n
(
x
k
-
x
¯
i
)
(
x
k
-
x
¯
j
)
n
-
1
Doc 41
0.1859
0.1859
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rank_correlation.html
Γ
=
∑
(
r
j
-
r
i
)
(
s
j
-
s
i
)
∑
(
r
j
-
r
i
)
2
Doc 42
0.1819
0.1819
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Dunnett's_test.html
s
2
=
∑
i
=
0
p
∑
j
=
1
N
i
(
X
i
j
-
X
i
¯
)
n
Doc 43
0.1786
0.1786
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Variance.html
σ
y
2
=
1
n
∑
i
=
1
n
(
y
i
-
y
¯
)
2
=
(
1
n
∑
i
=
1
n
y
i
2
)
-
y
¯
2
Doc 44
0.1678
0.3255
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Pooled_variance.html
s
p
2
=
∑
i
=
1
k
(
n
i
-
1
)
s
i
2
∑
i
=
1
k
n
i
s
p
2
=
∑
i
=
1
k
(
n
i
-
1
)
s
i
2
∑
i
=
1
k
(
n
i
-
1
)
Doc 45
0.1628
0.1628
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Normal_distribution.html
∑
i
=
1
n
(
x
i
-
μ
)
2
=
∑
i
=
1
n
(
x
i
-
x
¯
)
2
+
n
(
x
¯
-
μ
)
2
Doc 46
0.1609
0.1609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Tukey's_test_of_additivity.html
S
S
A
B
≡
(
∑
i
j
Y
i
j
(
Y
¯
i
⋅
-
Y
¯
⋅
⋅
)
(
Y
¯
⋅
j
-
Y
¯
⋅
⋅
)
)
2
∑
i
(
Y
¯
i
⋅
-
Y
¯
⋅
⋅
)
2
∑
j
(
Y
¯
⋅
j
-
Y
¯
⋅
⋅
)
2
Doc 47
0.1537
0.1537
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Fixed_effects_model.html
=
[
∑
i
=
1
N
(
x
i
2
-
x
i
1
)
(
x
i
2
-
x
i
1
)
′
]
-
1
∑
i
=
1
N
(
x
i
2
-
x
i
1
)
(
y
i
2
-
y
i
1
)
=
F
D
T
=
2
Doc 48
0.1529
0.1529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Pythagorean_theorem.html
(
a
1
-
b
1
)
2
+
(
a
2
-
b
2
)
2
+
⋯
+
(
a
n
-
b
n
)
2
=
∑
i
=
1
n
(
a
i
-
b
i
)
2
.
Doc 49
0.1440
0.2815
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Omnibus_test.html
F
=
∑
i
=
1
n
(
y
i
^
-
y
¯
)
2
/
k
∑
j
=
1
k
∑
i
=
1
n
j
(
y
i
j
-
y
i
^
)
2
/
(
n
-
k
-
1
)
F
=
∑
j
=
1
k
n
j
(
y
¯
j
-
y
¯
)
2
/
(
k
-
1
)
∑
j
=
1
k
∑
i
=
1
n
j
(
y
i
j
-
y
¯
j
)
2
/
(
n
-
k
)
Doc 50
0.1408
0.1408
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Kruskal–Wallis_one-way_analysis_of_variance.html
K
=
(
N
-
1
)
∑
i
=
1
g
n
i
(
r
¯
i
⋅
-
r
¯
)
2
∑
i
=
1
g
∑
j
=
1
n
i
(
r
i
j
-
r
¯
)
2
,
Doc 51
0.1394
0.1394
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Antiderivative.html
∑
i
=
1
n
f
(
x
i
*
)
(
x
i
-
x
i
-
1
)
Doc 52
0.1386
0.1386
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Cauchy–Schwarz_inequality.html
∑
i
=
1
n
x
i
2
∑
i
=
1
n
y
i
2
-
(
∑
i
=
1
n
x
i
y
i
)
2
≥
0.
Doc 53
0.1382
0.2585
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cochran's_theorem.html
∑
(
X
i
-
μ
)
2
=
∑
(
X
i
-
X
¯
+
X
¯
-
μ
)
2
∑
(
X
i
-
μ
)
2
=
∑
(
X
i
-
X
¯
)
2
+
∑
(
X
¯
-
μ
)
2
+
2
∑
(
X
i
-
X
¯
)
(
X
¯
-
μ
)
.
Doc 54
0.1316
0.1316
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Signal-to-noise_ratio_(imaging).html
μ
sig
=
∑
i
=
1
n
(
X
i
-
f
i
)
n
μ
bkg
=
∑
i
=
1
n
(
X
i
-
f
i
)
n
Doc 55
0.1310
0.1310
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hypergeometric_distribution.html
(
N
-
2
K
)
(
N
-
1
)
1
2
(
N
-
2
n
)
[
n
K
(
N
-
K
)
(
N
-
n
)
]
1
2
(
N
-
2
)
Doc 56
0.1267
0.1267
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Recurrence_quantification_analysis.html
TREND
=
∑
i
=
1
N
~
(
i
-
N
~
/
2
)
(
R
R
i
-
⟨
R
R
i
⟩
)
∑
i
=
1
N
~
(
i
-
N
~
/
2
)
2
,
Doc 57
0.1244
0.2480
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Moran's_I.html
I
=
N
∑
i
∑
j
w
i
j
∑
i
∑
j
w
i
j
(
X
i
-
X
¯
)
(
X
j
-
X
¯
)
∑
i
(
X
i
-
X
¯
)
2
S
3
=
N
-
1
∑
i
(
x
i
-
x
¯
)
4
(
N
-
1
∑
i
(
x
i
-
x
¯
)
2
)
2
Doc 58
0.1231
0.1231
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Brahmagupta.html
(
t
-
p
)
(
t
-
q
)
(
t
-
r
)
(
t
-
s
)
.
Doc 59
0.1221
0.1221
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Correlation_ratio.html
η
2
=
∑
x
n
x
(
y
¯
x
-
y
¯
)
2
∑
x
,
i
(
y
x
i
-
y
¯
)
2
Doc 60
0.1218
0.1218
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Gauss–Markov_theorem.html
∑
i
=
1
n
(
y
i
-
y
^
i
)
2
=
∑
i
=
1
n
(
y
i
-
∑
j
=
1
K
β
^
j
X
i
j
)
2
.
Doc 61
0.1143
0.1143
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Jarque–Bera_test.html
C
=
μ
^
4
σ
^
4
=
1
n
∑
i
=
1
n
(
x
i
-
x
¯
)
4
(
1
n
∑
i
=
1
n
(
x
i
-
x
¯
)
2
)
2
,
Doc 62
0.1122
0.1122
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Bessel's_correction.html
s
n
2
=
1
n
∑
i
=
1
n
(
x
i
-
x
¯
)
2
=
∑
i
=
1
n
(
x
i
2
)
n
-
(
∑
i
=
1
n
x
i
)
2
n
2
Doc 63
0.1113
0.1113
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Nakayama_lemma.html
∑
i
=
1
n
x
i
(
1
-
k
i
)
(
1
-
k
j
)
-
1
=
0
Doc 64
0.1030
0.1030
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Maximum_likelihood.html
σ
^
2
=
1
n
∑
i
=
1
n
(
μ
-
δ
i
)
2
-
1
n
2
∑
i
=
1
n
∑
j
=
1
n
(
μ
-
δ
i
)
(
μ
-
δ
j
)
.