# set terminal pngcairo transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 # set output 'prob.25.png' set format x "%2.0f" set format y "%3.2f" set key fixed right bottom vertical Right noreverse enhanced autotitle box lt black linewidth 1.000 dashtype solid unset key set style increment default set samples 13, 13 set ytics norangelimit 0.00000,0.030486,0.304860 set title "hypergeometric PDF with N = 75, C = 25, d = 10" set trange [ -0.200000 : 3.20913 ] noreverse nowriteback set xlabel "k ->" set xrange [ -1.00000 : 11.0000 ] noreverse nowriteback set x2range [ * : * ] noreverse writeback set ylabel "probability density ->" set yrange [ 0.00000 : 0.304860 ] noreverse nowriteback set y2range [ * : * ] noreverse writeback set zrange [ * : * ] noreverse writeback set cbrange [ * : * ] noreverse writeback set rrange [ * : * ] noreverse writeback isint(x)=(int(x)==x) Binv(p,q)=exp(lgamma(p+q)-lgamma(p)-lgamma(q)) arcsin(x,r)=r<=0?1/0:abs(x)>r?0.0:invpi/sqrt(r*r-x*x) beta(x,p,q)=p<=0||q<=0?1/0:x<0||x>1?0.0:Binv(p,q)*x**(p-1.0)*(1.0-x)**(q-1.0) binom(x,n,p)=p<0.0||p>1.0||n<0||!isint(n)?1/0: !isint(x)?1/0:x<0||x>n?0.0:exp(lgamma(n+1)-lgamma(n-x+1)-lgamma(x+1) +x*log(p)+(n-x)*log(1.0-p)) cauchy(x,a,b)=b<=0?1/0:b/(pi*(b*b+(x-a)**2)) chisq(x,k)=k<=0||!isint(k)?1/0: x<=0?0.0:exp((0.5*k-1.0)*log(x)-0.5*x-lgamma(0.5*k)-k*0.5*log2) erlang(x,n,lambda)=n<=0||!isint(n)||lambda<=0?1/0: x<0?0.0:x==0?(n==1?real(lambda):0.0):exp(n*log(lambda)+(n-1.0)*log(x)-lgamma(n)-lambda*x) extreme(x,mu,alpha)=alpha<=0?1/0:alpha*(exp(-alpha*(x-mu)-exp(-alpha*(x-mu)))) f(x,d1,d2)=d1<=0||!isint(d1)||d2<=0||!isint(d2)?1/0: Binv(0.5*d1,0.5*d2)*(real(d1)/d2)**(0.5*d1)*x**(0.5*d1-1.0)/(1.0+(real(d1)/d2)*x)**(0.5*(d1+d2)) gmm(x,rho,lambda)=rho<=0||lambda<=0?1/0: x<0?0.0:x==0?(rho>1?0.0:rho==1?real(lambda):1/0): exp(rho*log(lambda)+(rho-1.0)*log(x)-lgamma(rho)-lambda*x) geometric(x,p)=p<=0||p>1?1/0: !isint(x)?1/0:x<0||p==1?(x==0?1.0:0.0):exp(log(p)+x*log(1.0-p)) halfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:sqrt2invpi/sigma*exp(-0.5*(x/sigma)**2) hypgeo(x,N,C,d)=N<0||!isint(N)||C<0||C>N||!isint(C)||d<0||d>N||!isint(d)?1/0: !isint(x)?1/0:x>d||x>C||x<0||x1?1/0: !isint(x)?1/0:x<0?0.0:p==1?(x==0?1.0:0.0):exp(lgamma(r+x)-lgamma(r)-lgamma(x+1)+ r*log(p)+x*log(1.0-p)) nexp(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*exp(-lambda*x) normal(x,mu,sigma)=sigma<=0?1/0:invsqrt2pi/sigma*exp(-0.5*((x-mu)/sigma)**2) pareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:x=a?0.0:f==0?1.0/a:2.0/a*sin(f*pi*x/a)**2/(1-sin(twopi*f)) t(x,nu)=nu<0||!isint(nu)?1/0: Binv(0.5*nu,0.5)/sqrt(nu)*(1+real(x*x)/nu)**(-0.5*(nu+1.0)) triangular(x,m,g)=g<=0?1/0:x=m+g?0.0:1.0/g-abs(x-m)/real(g*g) uniform(x,a,b)=x<(a=(a>b?a:b)?0.0:1.0/abs(b-a) weibull(x,a,lambda)=a<=0||lambda<=0?1/0: x<0?0.0:x==0?(a>1?0.0:a==1?real(lambda):1/0): exp(log(a)+a*log(lambda)+(a-1)*log(x)-(lambda*x)**a) carcsin(x,r)=r<=0?1/0:x<-r?0.0:x>r?1.0:0.5+invpi*asin(x/r) cbeta(x,p,q)=ibeta(p,q,x) cbinom(x,n,p)=p<0.0||p>1.0||n<0||!isint(n)?1/0: !isint(x)?1/0:x<0?0.0:x>=n?1.0:ibeta(n-x,x+1.0,1.0-p) ccauchy(x,a,b)=b<=0?1/0:0.5+invpi*atan((x-a)/b) cchisq(x,k)=k<=0||!isint(k)?1/0:x<0?0.0:igamma(0.5*k,0.5*x) cerlang(x,n,lambda)=n<=0||!isint(n)||lambda<=0?1/0:x<0?0.0:igamma(n,lambda*x) cextreme(x,mu,alpha)=alpha<=0?1/0:exp(-exp(-alpha*(x-mu))) cf(x,d1,d2)=d1<=0||!isint(d1)||d2<=0||!isint(d2)?1/0:1.0-ibeta(0.5*d2,0.5*d1,d2/(d2+d1*x)) cgmm(x,rho,lambda)=rho<=0||lambda<=0?1/0:x<0?0.0:igamma(rho,x*lambda) cgeometric(x,p)=p<=0||p>1?1/0: !isint(x)?1/0:x<0||p==0?0.0:p==1?1.0:1.0-exp((x+1)*log(1.0-p)) chalfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:erf(x/sigma/sqrt2) chypgeo(x,N,C,d)=N<0||!isint(N)||C<0||C>N||!isint(C)||d<0||d>N||!isint(d)?1/0: !isint(x)?1/0:x<0||xd||x>C?1.0:hypgeo(x,N,C,d)+chypgeo(x-1,N,C,d) claplace(x,mu,b)=b<=0?1/0:(x1?1/0: !isint(x)?1/0:x<0?0.0:ibeta(r,x+1,p) cnexp(x,lambda)=lambda<=0?1/0:x<0?0.0:1-exp(-lambda*x) cpareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:xa?1.0:f==0?real(x)/a:(real(x)/a-sin(f*twopi*x/a)/(f*twopi))/(1.0-sin(twopi*f)/(twopi*f)) ct(x,nu)=nu<0||!isint(nu)?1/0:0.5+0.5*sgn(x)*(1-ibeta(0.5*nu,0.5,nu/(nu+x*x))) ctriangular(x,m,g)=g<=0?1/0: x=m+g?1.0:0.5+real(x-m)/g-(x-m)*abs(x-m)/(2.0*g*g) cuniform(x,a,b)=x<(a=(a>b?a:b)?1.0:real(x-a)/(b-a) cweibull(x,a,lambda)=a<=0||lambda<=0?1/0:x<0?0.0:1.0-exp(-(lambda*x)**a) gsampfunc(t,n) = t<0?0.5*1/(-t+1.0)**n:1.0-0.5*1/(t+1.0)**n keystr(rho,lambda) = sprintf("rho = %0.1f, lambda = %0.1f", rho, lambda) fourinvsqrtpi = 2.25675833419103 invpi = 0.318309886183791 invsqrt2pi = 0.398942280401433 log2 = 0.693147180559945 sqrt2 = 1.4142135623731 sqrt2invpi = 0.797884560802865 twopi = 6.28318530717959 eps = 1e-10 xmin = -1 xmax = 11 ymin = -5 ymax = 0.30485951131839 r = 2.0 mu = 3.33333333333333 sigma = 1.39712274047485 p = 0.333333333333333 q = 3.0 n = 2 a = 0 b = 2 k = 8 lambda = 2.0 l1 = 1.0 l2 = 1.0 alpha = 1.0 u = 0.0 df1 = 5.0 df2 = 9.0 rho = 6.0 r1 = 0.5 r2 = 1.0 r3 = 1.0 r4 = 1.3 r5 = 2.0 r6 = 4.0 r7 = 6.0 l3 = 1.3 l4 = 1.3 l5 = 2.0 l6 = 2.0 l7 = 2.0 s = 0.602810274989087 N = 75 C = 25 d = 10 plot hypgeo(x,N,C,d) with impulses