Scilab 5.3.3
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See the recommended documentation of this function
binomial
binomial distribution probabilities
Calling Sequence
pr=binomial(p,n)
Arguments
- pr
row vector with n+1 components
- p
real number in [0,1]
- n
an integer >= 1
Description
pr=binomial(p,n) returns the binomial probability
vector, i.e. pr(k+1) is the probability of
k success in n independent
Bernouilli trials with probability of success p. In
other words : pr(k+1) = probability(X=k) , with X a
random variable following the B(n,p) distribution, and numerically
:
Examples
// first example n=10;p=0.3; clf(); plot2d3(0:n,binomial(p,n)); // second example n=50;p=0.4; mea=n*p; sigma=sqrt(n*p*(1-p)); x=( (0:n)-mea )/sigma; clf() plot2d(x, sigma*binomial(p,n)); deff('y=Gauss(x)','y=1/sqrt(2*%pi)*exp(-(x.^2)/2)') plot2d(x, Gauss(x), style=2); // by binomial formula (Caution if big n) function pr=binomial2(p, n) x=poly(0,'x');pr=coeff((1-p+x)^n).*horner(x^(0:n),p); endfunction p=1/3;n=5; binomial(p,n)-binomial2(p,n) // by Gamma function: gamma(n+1)=n! (Caution if big n) p=1/3;n=5; Cnks=gamma(n+1)./(gamma(1:n+1).*gamma(n+1:-1:1)); x=poly(0,'x'); pr=Cnks.*horner(x.^(0:n).*(1-x)^(n:-1:0),p); pr-binomial(p,n)
See Also
| << Discrete mathematics | Discrete mathematics | factor >> |