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Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
binomial
2項分布確率
呼び出し手順
pr=binomial(p,n)
パラメータ
- pr
n+1 個の要素の行ベクトル
- p
[0,1]の範囲の実数
- n
整数 >= 1
説明
pr=binomial(p,n) は,
二項分布確率ベクトルを返します.
これは,
pr(k+1)が n
回の成功率pの独立ベルヌーイ試行において
k回成功する確率となる分布です.
言い換えると,,
XをB(n,p)分布に従うランダム変数とする時の
pr(k+1) = probability(X=k)で,
数値的には以下のようになります :
例
// 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)
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