# set terminal pngcairo transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 # set output 'prob.34.png' set format x "%.1f" set format y "%.1f" set key fixed right bottom vertical Right noreverse enhanced autotitle box lt black linewidth 1.000 dashtype solid set style increment default set xzeroaxis set yzeroaxis set zzeroaxis set title "maxwell CDF" set trange [ -0.200000 : 3.20913 ] noreverse nowriteback set xlabel "x ->" set xrange [ 0.00000 : 21.7553 ] noreverse nowriteback set x2range [ * : * ] noreverse writeback set ylabel "probability density ->" set yrange [ 0.00000 : 1.10000 ] 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 = 0 xmax = 6 ymin = -5 ymax = 2 r = 2.0 mu = 2.25675833419103 sigma = 1.3468792232857 p = 0.333333333333333 q = 3.0 n = 2 a = 1.5 b = 1.0 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 = 4.66878227507107 N = 75 C = 25 d = 10 m = 3.08021684891803 plot [xmin:xmax] [0:1.1] cmaxwell(x, 1.5) title "a = 1.5", cmaxwell(x, 1.0) title "a = 1.0", cmaxwell(x, 0.5) title "a = 0.5"