Combinatorial and statistical functions:
FACT(n) n! (n factorial) FACT(5)=120
FACT.L(n) log(n!) FACT.L(1000)=5912.1281784882
C(n,m) binomial coefficient C(10,5)=252
(See also COMB?)
Binomial distribution BIN(n,p):
BIN.f(n,p,x) probability of x BIN.f(4,1/2,0)=0.0625
BIN.F(n,p,x) distribution function BIN.F(4,1/2,3)=0.9375
BIN.G(n,p,y) inverse distribution function BIN.G(4,1/2,0.9375)=3
Poisson distribution POISSON(a):
POISSON.f(a,x) probability of x POISSON.f(5,5)=0.17546736976785
POISSON.F(a,x) distribution function POISSON.F(5,5)=0.61596065483306
POISSON.G(a,y) inverse distribution function POISSON.G(5,0.61)=5
Normal distribution N(m,s^2):
N.f(m,s^2,x) density function N.f(0,1,0)=0.39894228040143
N.F(m,s^2,x) distribution function N.F(0,1,2)=0.97724986805182
N.G(m,s^2,y) inverse distribution function N.G(0,1,0.995)=2.5758293035
t distribution function with n degrees of freedom:
t.f(n,x) density function t.f(30,0)=0.3956321848941
t.F(n,x) distribution function t.F(30,2)=0.97268747751851
t.G(n,y) inverse distribution function t.G(30,0.97)=1.9546454957885
Chi^2 distribution function with n degrees of freedom:
CHI2.f(n,x) density function CHI2.f(10,10)=0.08773368488393
CHI2.F(n,x) distribution function CHI2.F(10,10)=0.55950671493479
CHI2.G(n,y) inverse distribution function CHI2.G(10,0.97)=19.921910008236
Gamma distribution with paramaters a,b:
density f(x)=x^(a-1)*exp(-x/b)/[b^a*gamma(a)], x>0
gamma.f(lambda,k,x) density function gamma.f(5,2,10)=0.08773368488393
gamma.F(lambda,k,x) distribution function gamma.F(5,2,10)=0.55950671493479
gamma.G(lambda,k,x) inv.distribution function gamma.G(5,2,0.97)=19.921910008236
Relations:
gamma.f(a,b,x)=2/b*chi2.f(2*a,2*x/b)
gamma.F(a,b,x)=chi2.F(2*a,2*x/b)
gamma.G(a,b,x)=b/2*chi2.G(2*a,x)
F distribution function with m and n degrees of freedom:
F.f(m,n,x) density function F.f(5,6,1)=0.44505077818904
F.F(m,n,x) distribution function F.F(5,6,10)=0.99288015699002
F.G(m,n,y) inverse distribution function F.G(5,6,0.993)=10.066447766898
Beta distribution with parameters a,b:
density f(x)=gamma(a+b)/[gamma(a)*gamma(b)]*x^(a-1)*(1-x)^(b-1), 0<x<1
beta.f(a,b,x) density function beta.f(2,3,0.5)=1.5
beta.F(a,b,x) distribution function beta.F(2,3,0.5)=0.6875
beta.G(a,b,x) inverse distribution function beta.G(2,3,0.6875)=0.5
Weibull distribution with parameters a,b:
distribution function F(x)=1-exp[-(a*x)^b], x>0
Weibull.f(a,b,x) density function Weibull.f(1,2,1)=0.73575888234288
Weibull.F(a,b,x) distribution function Weibull.F(1,2,1)=0.63212055882856
Weibull.G(a,b,x) inverse distribution function Weibull.G(1,2,0.6321)=0.99997205804533
Weibull(a,1) is exponential distribution with parameter a.
Exponential distribution with parameter a:
exp.f(a,x), exp.F(a,x), exp.G(a,x) are available.
L = More information about library functions
D = More information on probability distributions
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