#!/usr/local/bin/gnuplot -persist
# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'random.5.png'
set grid nopolar
set grid xtics nomxtics ytics nomytics noztics nomztics nortics nomrtics \
 nox2tics nomx2tics noy2tics nomy2tics nocbtics nomcbtics
set grid layerdefault   lt 0 linecolor 0 linewidth 0.500,  lt 0 linecolor 0 linewidth 0.500
set key bmargin right vertical Right noreverse enhanced autotitle nobox
unset parametric
set view 68, 28, 1.4, 0.9
set samples 200, 200
set zzeroaxis lt black linewidth 1.000 dashtype solid
set xyplane at 0
set xtics axis in scale 1,0.5 nomirror norotate  autojustify
set ytics axis in scale 1,0.5 nomirror norotate  autojustify
set ztics axis in scale 1,0.5 nomirror norotate  autojustify
set title "Histogram of distance from origin of\n3000 multivariate unit variance samples" 
set title  offset graph 0, 0.15, 0 font "" textcolor lt -1 norotate
set xrange [ 0.00000 : 4.50000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set yrange [ 0.00000 : 0.650000 ] noreverse nowriteback
set y2range [ * : * ] noreverse writeback
set zrange [ -4.00000 : 4.00000 ] noreverse nowriteback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
tstring(n) = sprintf("Histogram of distance from origin of\n%d multivariate unit variance samples", n)
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||x<d-(N-C)?0.0:exp(lgamma(C+1)-lgamma(C-x+1)-lgamma(x+1)+  lgamma(N-C+1)-lgamma(d-x+1)-lgamma(N-C-d+x+1)+lgamma(N-d+1)+lgamma(d+1)-lgamma(N+1))
laplace(x,mu,b)=b<=0?1/0:0.5/b*exp(-abs(x-mu)/b)
logistic(x,a,lambda)=lambda<=0?1/0:lambda*exp(-lambda*(x-a))/(1.0+exp(-lambda*(x-a)))**2
lognormal(x,mu,sigma)=sigma<=0?1/0:  x<0?0.0:invsqrt2pi/sigma/x*exp(-0.5*((log(x)-mu)/sigma)**2)
maxwell(x,a)=a<=0?1/0:x<0?0.0:fourinvsqrtpi*a**3*x*x*exp(-a*a*x*x)
negbin(x,r,p)=r<=0||!isint(r)||p<=0||p>1?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:real(b)/x*(real(a)/x)**b
poisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:exp(x*log(mu)-lgamma(x+1)-mu)
rayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*2.0*x*exp(-lambda*x*x)
sine(x,f,a)=a<=0?1/0:  x<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||x>=m+g?0.0:1.0/g-abs(x-m)/real(g*g)
uniform(x,a,b)=x<(a<b?a:b)||x>=(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||x<d-(N-C)?0.0:x>d||x>C?1.0:hypgeo(x,N,C,d)+chypgeo(x-1,N,C,d)
claplace(x,mu,b)=b<=0?1/0:(x<mu)?0.5*exp((x-mu)/b):1.0-0.5*exp(-(x-mu)/b)
clogistic(x,a,lambda)=lambda<=0?1/0:1.0/(1+exp(-lambda*(x-a)))
clognormal(x,mu,sigma)=sigma<=0?1/0:x<=0?0.0:cnormal(log(x),mu,sigma)
cnormal(x,mu,sigma)=sigma<=0?1/0:0.5+0.5*erf((x-mu)/sigma/sqrt2)
cmaxwell(x,a)=a<=0?1/0:x<0?0.0:igamma(1.5,a*a*x*x)
cnegbin(x,r,p)=r<=0||!isint(r)||p<=0||p>1?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:x<a?0.0:1.0-(real(a)/x)**b
cpoisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:1-igamma(x+1.0,mu)
crayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:1.0-exp(-lambda*x*x)
csine(x,f,a)=a<=0?1/0:  x<0?0.0:x>a?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?0.0: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<b?a:b)?0.0:x>=(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)
bin(x) = (1.0/scale)*floor(x*scale)
NO_ANIMATION = 1
nsamp = 3000
fourinvsqrtpi = 2.25675833419103
invpi = 0.318309886183791
invsqrt2pi = 0.398942280401433
log2 = 0.693147180559945
sqrt2 = 1.4142135623731
sqrt2invpi = 0.797884560802865
twopi = 6.28318530717959
binwidth = 20
xlow = 0.0
xhigh = 4.5
scale = 4.44444444444444
oneplot = 1
rlow = -4.0
rhigh = 4.0
## Last datafile plotted: "$random"
plot $random using (bin(sqrt($1**2+$2**2+$3**2))):(1.0*scale/nsamp) every :::::0 smooth frequency with steps         title "scaled bin frequency",         maxwell(x, 1/sqrt(2)) with lines title "Maxwell p.d.f.",         $random using (sqrt($1**2+$2**2+$3**2)):(scale/nsamp) bins=25 binrange [xlow:xhigh] with impulse lw 5 title "assign samples to 25 bins"