# set terminal canvas  rounded size 600,400 enhanced fsize 10 lw 1.6 fontscale 1 name "random_5" jsdir "."
# set output 'random.5.js'
set grid nopolar
set grid xtics nomxtics ytics nomytics noztics nomztics \
 nox2tics nomx2tics noy2tics nomy2tics nocbtics nomcbtics
set grid layerdefault   lt 0 linewidth 0.500,  lt 0 linewidth 0.500
set key bmargin right vertical Right noreverse enhanced autotitle nobox
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 "" norotate
set xrange [ 0.00000 : 4.50000 ] noreverse nowriteback
set yrange [ 0.00000 : 0.650000 ] noreverse nowriteback
set zrange [ -4.00000 : 4.00000 ] noreverse nowriteback
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)
nsamp = 3000
i = 3001
GPFUN_tstring = "tstring(n) = sprintf(\"Histogram of distance from origin of\\n%d multivariate unit variance samples\", n)"
u = 0.0
GPFUN_isint = "isint(x)=(int(x)==x)"
fourinvsqrtpi = 2.25675833419103
invpi = 0.318309886183791
invsqrt2pi = 0.398942280401433
log2 = 0.693147180559945
sqrt2 = 1.4142135623731
sqrt2invpi = 0.797884560802865
twopi = 6.28318530717959
GPFUN_Binv = "Binv(p,q)=exp(lgamma(p+q)-lgamma(p)-lgamma(q))"
GPFUN_arcsin = "arcsin(x,r)=r<=0?1/0:abs(x)>r?0.0:invpi/sqrt(r*r-x*x)"
GPFUN_beta = "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)"
GPFUN_binom = "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))"
GPFUN_cauchy = "cauchy(x,a,b)=b<=0?1/0:b/(pi*(b*b+(x-a)**2))"
GPFUN_chisq = "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)"
GPFUN_erlang = "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)"
GPFUN_extreme = "extreme(x,mu,alpha)=alpha<=0?1/0:alpha*(exp(-alpha*(x-mu)-exp(-alpha*(x-mu))))"
GPFUN_f = "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))"
GPFUN_gmm = "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)"
GPFUN_geometric = "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))"
GPFUN_halfnormal = "halfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:sqrt2invpi/sigma*exp(-0.5*(x/sigma)**2)"
GPFUN_hypgeo = "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))"
GPFUN_laplace = "laplace(x,mu,b)=b<=0?1/0:0.5/b*exp(-abs(x-mu)/b)"
GPFUN_logistic = "logistic(x,a,lambda)=lambda<=0?1/0:lambda*exp(-lambda*(x-a))/(1.0+exp(-lambda*(x-a)))**2"
GPFUN_lognormal = "lognormal(x,mu,sigma)=sigma<=0?1/0:  x<0?0.0:invsqrt2pi/sigma/x*exp(-0.5*((log(x)-mu)/sigma)**2)"
GPFUN_maxwell = "maxwell(x,a)=a<=0?1/0:x<0?0.0:fourinvsqrtpi*a**3*x*x*exp(-a*a*x*x)"
GPFUN_negbin = "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))"
GPFUN_nexp = "nexp(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*exp(-lambda*x)"
GPFUN_normal = "normal(x,mu,sigma)=sigma<=0?1/0:invsqrt2pi/sigma*exp(-0.5*((x-mu)/sigma)**2)"
GPFUN_pareto = "pareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:x<a?0:real(b)/x*(real(a)/x)**b"
GPFUN_poisson = "poisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:exp(x*log(mu)-lgamma(x+1)-mu)"
GPFUN_rayleigh = "rayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*2.0*x*exp(-lambda*x*x)"
GPFUN_sine = "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))"
GPFUN_t = "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))"
GPFUN_triangular = "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)"
GPFUN_uniform = "uniform(x,a,b)=x<(a<b?a:b)||x>=(a>b?a:b)?0.0:1.0/abs(b-a)"
GPFUN_weibull = "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)"
GPFUN_carcsin = "carcsin(x,r)=r<=0?1/0:x<-r?0.0:x>r?1.0:0.5+invpi*asin(x/r)"
GPFUN_cbeta = "cbeta(x,p,q)=ibeta(p,q,x)"
GPFUN_cbinom = "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)"
GPFUN_ccauchy = "ccauchy(x,a,b)=b<=0?1/0:0.5+invpi*atan((x-a)/b)"
GPFUN_cchisq = "cchisq(x,k)=k<=0||!isint(k)?1/0:x<0?0.0:igamma(0.5*k,0.5*x)"
GPFUN_cerlang = "cerlang(x,n,lambda)=n<=0||!isint(n)||lambda<=0?1/0:x<0?0.0:igamma(n,lambda*x)"
GPFUN_cextreme = "cextreme(x,mu,alpha)=alpha<=0?1/0:exp(-exp(-alpha*(x-mu)))"
GPFUN_cf = "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))"
GPFUN_cgmm = "cgmm(x,rho,lambda)=rho<=0||lambda<=0?1/0:x<0?0.0:igamma(rho,x*lambda)"
GPFUN_cgeometric = "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))"
GPFUN_chalfnormal = "chalfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:erf(x/sigma/sqrt2)"
GPFUN_chypgeo = "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)"
GPFUN_claplace = "claplace(x,mu,b)=b<=0?1/0:(x<mu)?0.5*exp((x-mu)/b):1.0-0.5*exp(-(x-mu)/b)"
GPFUN_clogistic = "clogistic(x,a,lambda)=lambda<=0?1/0:1.0/(1+exp(-lambda*(x-a)))"
GPFUN_clognormal = "clognormal(x,mu,sigma)=sigma<=0?1/0:x<=0?0.0:cnormal(log(x),mu,sigma)"
GPFUN_cmaxwell = "cmaxwell(x,a)=a<=0?1/0:x<0?0.0:igamma(1.5,a*a*x*x)"
GPFUN_cnegbin = "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)"
GPFUN_cnexp = "cnexp(x,lambda)=lambda<=0?1/0:x<0?0.0:1-exp(-lambda*x)"
GPFUN_cnormal = "cnormal(x,mu,sigma)=sigma<=0?1/0:0.5+0.5*erf((x-mu)/sigma/sqrt2)"
GPFUN_cpareto = "cpareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:x<a?0.0:1.0-(real(a)/x)**b"
GPFUN_cpoisson = "cpoisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:1-igamma(x+1.0,mu)"
GPFUN_crayleigh = "crayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:1.0-exp(-lambda*x*x)"
GPFUN_csine = "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))"
GPFUN_ct = "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)))"
GPFUN_ctriangular = "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)"
GPFUN_cuniform = "cuniform(x,a,b)=x<(a<b?a:b)?0.0:x>=(a>b?a:b)?1.0:real(x-a)/(b-a)"
GPFUN_cweibull = "cweibull(x,a,lambda)=a<=0||lambda<=0?1/0:x<0?0.0:1.0-exp(-(lambda*x)**a)"
binwidth = 20
xlow = 0.0
xhigh = 4.5
scale = 4.44444444444444
GPFUN_bin = "bin(x) = (1.0/scale)*floor(x*scale)"
x = 0.0
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 with impulse lw 5 title "assign samples to 25 bins"