統計-数式
以下は、Tutorialspoint統計チュートリアルで使用される統計式のリストです。各数式は、数式の使用方法を説明するWebページにリンクされています。
A
Adjusted R-Squared -$ {R_ {adj} ^ 2 = 1-[\ frac {（1-R ^ 2）（n-1）} {nk-1}]} $
Arithmetic Mean -$ \ bar {x} = \ frac {_ {\ sum {x}}} {N} $
Arithmetic Median -中央値= $ \ frac {N + 1} {2}）^ {th} \ item $の値
Arithmetic Range -$ {Coefficient \ of \ Range = \ frac {LS} {L + S}} $
B
Best Point Estimation -$ {MLE = \ frac {S} {T}} $
Binomial Distribution -$ {P（Xx）} = ^ {n} {C_x} {Q ^ {nx}}。{p ^ x} $
C
Chebyshev's Theorem -$ {1- \ frac {1} {k ^ 2}} $
Circular Permutation -$ {P_n =（n-1）！} $
Cohen's kappa coefficient -$ {k = \ frac {p_0 --p_e} {1-p_e} = 1- \ frac {1-p_o} {1-p_e}} $
Combination -$ {C（n、r）= \ frac {n！} {r！（nr）！}} $
Combination with replacement -$ {^ nC_r = \ frac {（n + r-1）！} {r！（n-1）！}} $
Continuous Uniform Distribution --f（x）= $ \ begin {cases} 1 /（ba）、＆\ text {when $ a \ le x \ le b $} \\ 0、＆\ text {when $ x \ lt a $または$ x \ gt b $} \ end {cases} $
Coefficient of Variation -$ {CV = \ frac {\ sigma} {X} \ times 100} $
Correlation Co-efficient -$ {r = \ frac {N \ sum xy-（\ sum x）（\ sum y）} {\ sqrt {[N \ sum x ^ 2-（\ sum x）^ 2] [N \ sum y ^ 2-（\ sum y）^ 2]}}} $
Cumulative Poisson Distribution -$ {F（x、\ lambda）= \ sum_ {k = 0} ^ x \ frac {e ^ {-\ lambda} \ lambda ^ x} {k！}} $
D
Deciles Statistics-$ {D_i = l + \ frac {h} {f}（\ frac {iN} {10} --c）; i = 1,2,3 ...、9} $
Deciles Statistics-$ {D_i = l + \ frac {h} {f}（\ frac {iN} {10} --c）; i = 1,2,3 ...、9} $
F
Factorial-$ {n！= 1 \ times 2 \ times 3 ... \ times n} $
G
Geometric Mean -$ GM = \ sqrt [n] {x_1x_2x_3 ... x_n} $
Geometric Probability Distribution -$ {P（X = x）= p \ times q ^ {x-1}} $
Grand Mean -$ {X_ {GM} = \ frac {\ sum x} {N}} $
H
Harmonic Mean -$ HM = \ frac {W} {\ sum（\ frac {W} {X}）} $
Harmonic Mean -$ HM = \ frac {W} {\ sum（\ frac {W} {X}）} $
Hypergeometric Distribution -$ {h（x; N、n、K）= \ frac {[C（k、x）] [C（Nk、nx）]} {C（N、n）}} $
私
Interval Estimation -$ {\ mu = \ bar x \ pm Z _ {\ frac {\ alpha} {2}} \ frac {\ sigma} {\ sqrt n}} $
L
Logistic Regression -$ {\ pi（x）= \ frac {e ^ {\ alpha + \ beta x}} {1 + e ^ {\ alpha + \ beta x}}} $
M
Mean Deviation -$ {MD} = \ frac {1} {N} \ sum {| XA |} = \ frac {\ sum {| D |}} {N} $
Mean Difference -$ {Mean \ Difference = \ frac {\ sum x_1} {n}-\ frac {\ sum x_2} {n}} $
Multinomial Distribution -$ {P_r = \ frac {n！} {（n_1！）（n_2！）...（n_x！）} {P_1} ^ {n_1} {P_2} ^ {n_2} ... {P_x} ^ { n_x}} $
N
Negative Binomial Distribution -$ {f（x）= P（X = x）=（x-1r-1）（1-p）x-rpr} $
Normal Distribution -$ {y = \ frac {1} {\ sqrt {2 \ pi}} e ^ {\ frac {-（x- \ mu）^ 2} {2 \ sigma}}} $
O
One Proportion Z Test -$ {z = \ frac {\ hat p -p_o} {\ sqrt {\ frac {p_o（1-p_o）} {n}}}} $
P
Permutation -$ {{^ nP_r = \ frac {n！} {（nr）！}} $
Permutation with Replacement -$ {^ nP_r = n ^ r} $
Poisson Distribution -$ {P（Xx）} = {e ^ {-m}}。\ frac {m ^ x} {x！} $
probability -$ {P（A）= \ frac {Number \ of \ favourable \ Cases} {Total \ number \ of \ equally \おそらく\ cases} = \ frac {m} {n}} $
Probability Additive Theorem -$ {P（A \または\ B）= P（A）+ P（B）\\ [7pt] P（A \ cup B）= P（A）+ P（B）} $
Probability Multiplicative Theorem -$ {P（A \ and \ B）= P（A）\ times P（B）\\ [7pt] P（AB）= P（A）\ times P（B）} $
Probability Bayes Theorem -$ {P（A_i / B）= \ frac {P（A_i）\ times P（B / A_i）} {\ sum_ {i = 1} ^ k P（A_i）\ times P（B / A_i）}} $
Probability Density Function -$ {P（a \ le X \ le b）= \ int_a ^ bf（x）d_x} $
R
Reliability Coefficient -$ {Reliability \ Coefficient、\ RC =（\ frac {N} {（N-1）}）\ times（\ frac {（Total \ Variance \ --Sum \ of \ Variance）} {Total Variance}）} $
Residual Sum of Squares -$ {RSS = \ sum_ {i = 0} ^ n（\ epsilon_i）^ 2 = \ sum_ {i = 0} ^ n（y_i-（\ alpha + \ beta x_i））^ 2} $
S
Shannon Wiener Diversity Index -$ {H = \ sum [（p_i）\ times ln（p_i）]} $
Standard Deviation -$ \ sigma = \ sqrt {\ frac {\ sum_ {i = 1} ^ n {（x- \ bar x）^ 2}} {N-1}} $
Standard Error ( SE ) -$ SE_ \ bar {x} = \ frac {s} {\ sqrt {n}} $
Sum of Square -$ {Sum \ of \ Squares \ = \ sum（x_i- \ bar x）^ 2} $
T
Trimmed Mean -$ \ mu = \ frac {\ sum {X_i}} {n} $