# set terminal png transparent nocrop enhanced font arial 8 size 420,320 # set output 'prob.26.png' set format x "%.1f" set format y "%.2f" unset key set xzeroaxis lt 0 lw 1.000 set yzeroaxis lt 0 lw 1.000 set title "laplace (or double exponential) PDF with a = 0, b = 1" 0.000000,0.000000 font "" set xlabel "x ->" 0.000000,0.000000 font "" set xrange [ -5.65685 : 5.65685 ] noreverse nowriteback set ylabel "probability density ->" 0.000000,0.000000 font "" set yrange [ 0.00000 : 0.550000 ] noreverse nowriteback Binv(p,q)=exp(lgamma(p+q)-lgamma(p)-lgamma(q)) arcsin(x)=invpi/sqrt(r*r-x*x) beta(x)=Binv(p,q)*x**(p-1.0)*(1.0-x)**(q-1.0) bin_s(x)=n!/(n-int(x))!/int(x)!*p**int(x)*(1.0-p)**(n-int(x)) bin_l(x)=exp(lgamma(n+1)-lgamma(n-int(x)+1)-lgamma(int(x)+1)+int(x)*log(p)+(n-int(x))*log(1.0-p)) binom(x)=(n<20)?bin_s(x):bin_l(x) cauchy(x)=b/(pi*(b*b+(x-a)**2)) chi(x)=exp((0.5*df1-1.0)*log(x)-0.5*x-lgamma(0.5*df1)-df1*0.5*log2) erlang(x)=lambda**n/(n-1)!*x**(n-1)*exp(-lambda*x) extreme(x)=alpha*(exp(-alpha*(x-u)-exp(-alpha*(x-u)))) f(x)=Binv(0.5*df1,0.5*df2)*(df1/df2)**(0.5*df1)*x**(0.5*df1-1.0)/(1.0+df1/df2*x)**(0.5*(df1+df2)) g(x)=exp(rho*log(lambda)+(rho-1.0)*log(x)-lgamma(rho)-lambda*x) geometric(x)=exp(log(p)+int(x)*log(1.0-p)) halfnormal(x)=sqrt2invpi/sigma*exp(-0.5*(x/sigma)**2) hypgeo(x)=(int(x)>mm||int(x)