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Search
Returned 99 matches (100 formulae, 64 docs)
Lookup 696.779 ms, Re-ranking 5570.446 ms
Found 813116 tuple postings, 162979 formulae, 20880 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
0.0000
28.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dimensionless_quantity.html
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1
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Doc 2
1.0000
-32.0000
35.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Correlation_and_dependence.html
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,
Doc 3
0.7176
-15.0000
23.0000
0.7176
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Fisher_transformation.html
r
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Doc 4
0.7176
-19.0000
25.0000
1.3159
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html
r
=
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Doc 5
0.5764
-19.0000
19.0000
0.5764
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Assortativity.html
r
(
α
,
β
)
=
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j
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Doc 6
0.5474
-34.0000
22.0000
0.5474
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Collaborative_filtering.html
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Doc 7
0.5404
-38.0000
20.0000
0.8106
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kurtosis.html
=
(
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k
2
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(
n
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)
(
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Doc 8
0.4116
-16.0000
14.0000
1.1290
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html
b
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Doc 9
0.4116
-31.0000
14.0000
0.7996
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hotelling's_T-squared_distribution.html
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=
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Doc 10
0.4116
-32.0000
14.0000
0.7996
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Simple_linear_regression.html
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Doc 11
0.4116
-53.0000
14.0000
0.4116
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Regression_toward_the_mean.html
β
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Doc 12
0.3989
-9.0000
13.0000
1.2789
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html
∑
i
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1
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/
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Doc 13
0.3880
-8.0000
13.0000
2.5851
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html
S
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=
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(
x
i
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x
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Σ
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1
(
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Doc 14
0.3880
-9.0000
12.0000
1.1873
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html
𝐐
=
1
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k
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1
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1
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(
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(
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k
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Doc 15
0.3880
-12.0000
13.0000
0.3880
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Pivotal_quantity.html
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1
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1
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(
X
i
-
X
¯
)
(
Y
i
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Y
¯
)
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X
s
Y
Doc 16
0.3880
-14.0000
13.0000
1.1641
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Multivariate_normal_distribution.html
s
y
m
b
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l
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1
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Doc 17
0.3880
-23.0000
9.0000
0.3880
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Errors-in-variables_models.html
β
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1
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1
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t
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(
y
t
-
y
¯
)
1
T
∑
t
=
1
T
(
x
t
-
x
¯
)
2
,
Doc 18
0.3516
-4.0000
10.0000
0.7033
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Conjugate_prior.html
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Doc 19
0.3409
-7.0000
10.0000
0.3409
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Linear_discriminant_analysis.html
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(
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i
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μ
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Doc 20
0.3379
-14.0000
13.0000
0.6553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html
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score
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(
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1
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Doc 21
0.3280
-3.0000
12.0000
0.3280
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sufficient_statistic.html
∑
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x
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x
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)
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θ
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=
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Doc 22
0.3280
-5.0000
12.0000
0.5612
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html
σ
2
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1
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)
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Doc 23
0.3173
-19.0000
10.0000
0.3173
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Reciprocity_(network_science).html
ρ
≡
∑
i
≠
j
(
a
i
j
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a
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)
(
a
j
i
-
a
¯
)
∑
i
≠
j
(
a
i
j
-
a
¯
)
2
Doc 24
0.3173
-25.0000
10.0000
0.3173
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Regression_analysis.html
β
1
^
=
∑
(
x
i
-
x
¯
)
(
y
i
-
y
¯
)
∑
(
x
i
-
x
¯
)
2
and
β
0
^
=
y
¯
-
β
1
^
x
¯
Doc 25
0.3074
-34.0000
11.0000
0.3074
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Experimental_uncertainty_analysis.html
σ
^
i
=
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k
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1
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x
k
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x
¯
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)
2
n
-
1
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^
i
,
j
=
∑
k
=
1
n
(
x
k
-
x
¯
i
)
(
x
k
-
x
¯
j
)
n
-
1
Doc 26
0.3043
-20.0000
11.0000
0.3043
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 27
0.2938
-14.0000
10.0000
0.2938
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 28
0.2830
-5.0000
13.0000
1.0523
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html
C
n
=
∑
i
=
1
n
(
x
i
-
x
¯
n
)
(
y
i
-
y
¯
n
)
s
2
=
∑
i
=
1
n
(
x
i
-
K
)
2
-
(
∑
i
=
1
n
(
x
i
-
K
)
)
2
/
n
n
-
1
.
variance
=
s
2
=
∑
i
=
1
n
(
x
i
-
x
¯
)
2
n
-
1
∑
i
=
1
n
(
x
i
-
x
¯
n
)
2
Doc 29
0.2830
-13.0000
12.0000
0.2830
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 30
0.2750
-33.0000
12.0000
0.5259
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Omnibus_test.html
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
)
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
)
Doc 31
0.2750
-42.0000
12.0000
0.2750
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 32
0.2702
0.0000
10.0000
0.5404
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Bias_of_an_estimator.html
∑
i
=
1
n
(
X
i
-
X
¯
)
2
1
n
∑
i
=
1
n
(
X
i
-
X
¯
)
2
<
1
n
∑
i
=
1
n
(
X
i
-
μ
)
2
,
Doc 33
0.2702
0.0000
10.0000
0.2702
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Partition_of_sums_of_squares.html
∑
i
=
1
n
(
y
i
-
y
¯
)
2
Doc 34
0.2702
-7.0000
10.0000
0.4472
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html
s
=
∑
i
=
1
n
(
x
i
-
x
¯
)
2
n
-
1
s
¯
i
=
∑
j
=
1
n
(
x
i
j
-
x
¯
i
)
2
n
-
1
Doc 35
0.2702
-7.0000
10.0000
0.2702
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Kuder–Richardson_Formula_20.html
σ
X
2
=
∑
i
=
1
n
(
X
i
-
X
¯
)
2
n
.
Doc 36
0.2702
-15.0000
8.0000
0.2702
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Gravitational_lensing_formalism.html
q
x
y
=
∑
(
x
-
x
¯
)
(
y
-
y
¯
)
I
(
x
,
y
)
∑
I
(
x
,
y
)
Doc 37
0.2702
-20.0000
10.0000
0.2702
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 38
0.2702
-32.0000
10.0000
0.2702
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 39
0.2702
-32.0000
10.0000
0.2702
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 40
0.2466
-29.0000
7.0000
0.4461
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 41
0.2466
-30.0000
8.0000
0.2466
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 42
0.2424
-16.0000
8.0000
0.2424
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 43
0.2337
-36.0000
10.0000
0.2337
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 44
0.2332
-32.0000
9.0000
0.2332
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 45
0.2332
-34.0000
9.0000
0.4351
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Mean_square_weighted_deviation.html
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
σ
2
=
∑
i
=
1
N
w
i
(
x
i
-
x
¯
*
)
2
∑
i
=
1
N
w
i
Doc 46
0.2264
-18.0000
12.0000
0.2264
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 47
0.2230
-6.0000
9.0000
0.4461
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 48
0.2230
-7.0000
9.0000
0.2230
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Probability_theory.html
Z
n
=
∑
i
=
1
n
(
X
i
-
μ
)
σ
n
Doc 49
0.2230
-15.0000
8.0000
0.4461
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 50
0.2230
-28.0000
7.0000
0.3989
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cochran's_theorem.html
∑
(
X
i
-
μ
)
2
=
∑
(
X
i
-
X
¯
)
2
+
∑
(
X
¯
-
μ
)
2
+
2
∑
(
X
i
-
X
¯
)
(
X
¯
-
μ
)
.
∑
(
X
i
-
μ
)
2
=
∑
(
X
i
-
X
¯
+
X
¯
-
μ
)
2
Doc 51
0.2184
-2.0000
10.0000
0.2184
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Absolute_value.html
∑
i
=
1
n
(
a
i
-
b
i
)
2
.
Doc 52
0.2184
-6.0000
9.0000
0.2184
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 53
0.2184
-29.0000
10.0000
0.2184
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 54
0.2184
-31.0000
8.0000
0.2184
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
)
.
Doc 55
0.2018
-6.0000
9.0000
0.2018
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/F-test.html
∑
i
j
(
Y
i
j
-
Y
¯
i
⋅
)
2
/
(
N
-
K
)
,
Doc 56
0.2018
-12.0000
8.0000
0.2018
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 57
0.1994
-19.0000
5.0000
0.1994
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 58
0.1942
-21.0000
9.0000
0.1942
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 59
0.1942
-23.0000
9.0000
0.1942
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 60
0.1942
-26.0000
7.0000
0.1942
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 61
0.1616
-9.0000
7.0000
0.1616
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Antiderivative.html
∑
i
=
1
n
f
(
x
i
*
)
(
x
i
-
x
i
-
1
)
Doc 62
0.1575
-12.0000
6.0000
0.1575
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 63
0.1452
-12.0000
7.0000
0.1452
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
0.1285
-12.0000
4.0000
0.1285
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Brahmagupta.html
(
t
-
p
)
(
t
-
q
)
(
t
-
r
)
(
t
-
s
)
.