| Jakelu |
Todennäköisyysjakautumistoiminto |
Haje
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| Jatkuva yhtenäinen laki |
f(x)=1b-klo{\ displaystyle f (x) = {\ frac {1} {ba}}} varten klo≤x≤b{\ displaystyle a \ leq x \ leq b}
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ln(b-klo){\ displaystyle \ ln (ba) \,}
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| Normaali laki |
f(x)=12πσ2exp(-(x-μ)22σ2){\ displaystyle f (x) = {\ frac {1} {\ sqrt {2 \ pi \ sigma ^ {2}}}} \ exp \ left (- {\ frac {(x- \ mu) ^ {2} } {2 \ sigma ^ {2}}} \ oikea)} |
ln(σ2πe){\ displaystyle \ ln \ left (\ sigma {\ sqrt {2 \, \ pi \, e}} \ oikea)}
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| Eksponentiaalinen laki |
f(x)=λexp(-λx){\ displaystyle f (x) = \ lambda \ exp \ vasen (- \ lambda x \ oikea)} |
1-lnλ{\ displaystyle 1- \ ln \ lambda \,}
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| Cauchyn laki |
f(x)=λπ1λ2+x2{\ displaystyle f (x) = {\ frac {\ lambda} {\ pi}} {\ frac {1} {\ lambda ^ {2} + x ^ {2}}}} |
ln(4πλ){\ displaystyle \ ln (4 \ pi \ lambda) \,}
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| Laki ² |
f(x)=12ei/2σeiΓ(ei/2)xei2-1exp(-x2σ2){\ displaystyle f (x) = {\ frac {1} {2 ^ {n / 2} \ sigma ^ {n} \ Gamma (n / 2)}} x ^ {{\ frac {n} {2}} -1} \ exp \ left (- {\ frac {x} {2 \ sigma ^ {2}}} \ oikea)} |
ln2σ2Γ(ei2)-(1-ei2)ψ(ei2)+ei2{\ displaystyle \ ln 2 \ sigma ^ {2} \ Gamma \ vasen ({\ frac {n} {2}} \ oikea) - \ vasen (1 - {\ frac {n} {2}} \ oikea) \ psi \ vasen ({\ frac {n} {2}} \ oikea) + {\ frac {n} {2}}}
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| Gammajakauma |
f(x)=xa-1exp(-xβ)βaΓ(a){\ displaystyle f (x) = {\ frac {x ^ {\ alpha -1} \ exp (- {\ frac {x} {\ beta}})} {\ beta ^ {\ alpha} \ Gamma (\ alfa )}}} |
ln(βΓ(a))+(1-a)ψ(a)+a{\ displaystyle \ ln (\ beta \ Gamma (\ alfa)) + (1- \ alfa) \ psi (\ alfa) + \ alfa \,}
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| Logistiikkalaki |
f(x)=e-x(1+e-x)2{\ displaystyle f (x) = {\ frac {e ^ {- x}} {(1 + e ^ {- x}) ^ {2}}}} |
2{\ displaystyle 2 \,}
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| Maxwell-Boltzmann -tilasto |
f(x)=4π-12β32x2exp(-βx2){\ displaystyle f (x) = 4 \ pi ^ {- {\ frac {1} {2}}} \ beta ^ {\ frac {3} {2}} x ^ {2} \ exp (- \ beta x ^ {2})} |
12lnπβ+y-1/2{\ displaystyle {\ frac {1} {2}} \ ln {\ frac {\ pi} {\ beta}} + \ gamma -1/2}
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| Pareto-jakelu |
f(x)=klokkloxklo+1{\ displaystyle f (x) = {\ frac {ak ^ {a}} {x ^ {a + 1}}}} |
lnkklo+1+1klo{\ displaystyle \ ln {\ frac {k} {a}} + 1 + {\ frac {1} {a}}}
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| Opiskelijan laki |
f(x)=(1+x2/ei)-ei+12eiB(12,ei2){\ displaystyle f (x) = {\ frac {(1 + x ^ {2} / n) ^ {- {\ frac {n + 1} {2}}}} {{\ sqrt {n}} B ( {\ frac {1} {2}}, {\ frac {n} {2}})}}} |
ei+12ψ(ei+12)-ψ(ei2)+lneiB(12,ei2){\ displaystyle {\ frac {n + 1} {2}} \ psi \ vasen ({\ frac {n + 1} {2}} \ oikea) - \ psi \ vasen ({\ frac {n} {2} } \ oikea) + \ ln {\ sqrt {n}} B \ vasen ({\ frac {1} {2}}, {\ frac {n} {2}} \ oikea)}
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| Weibull-jakauma |
f(x)=vs.axvs.-1exp(-xvs.a){\ displaystyle f (x) = {\ frac {c} {\ alpha}} x ^ {c-1} \ exp \ left (- {\ frac {x ^ {c}} {\ alpha}} \ oikea) } |
(vs.-1)yvs.+lna1/vs.vs.+1{\ displaystyle {\ frac {(c-1) \ gamma} {c}} + \ ln {\ frac {\ alpha ^ {1 / c}} {c}} + 1}
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| Moniulotteinen normaali laki |
fX(x1,...,xEI)={\ displaystyle f_ {X} (x_ {1}, \ pistettä, x_ {N}) =} 1(2π)EI/2|Σ|1/2exp(-12(x-μ)⊤Σ-1(x-μ)){\ displaystyle {\ frac {1} {(2 \ pi) ^ {N / 2} \ vasen | \ Sigma \ oikea | ^ {1/2}}} \ exp \ vasen (- {\ frac {1} { 2}} (x- \ mu) ^ {\ top} \ Sigma ^ {- 1} (x- \ mu) \ oikea)}
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12ln{(2πe)EI|Σ|}{\ displaystyle {\ frac {1} {2}} \ ln \ {(2 \ pi e) ^ {N} | \ Sigma | \}}
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