from numpy import *
from matplotlib.pyplot import *
from mpl_toolkits.axes_grid.axislines import SubplotZero

pdf = lambda s,m,x: exp(-(log(x)-m)**2 / (2.*s**2)) / ( x*sqrt(2.*pi*s**2) )

fig = figure(figsize=(7,7))
ax = SubplotZero(fig,111)
fig.add_subplot(ax)

for direction in ["xzero","yzero"]:
        ax.axis[direction].set_visible(True)
        ax.axis[direction].set_axisline_style("->")
for direction in ["top","bottom","left","right"]:
        ax.axis[direction].set_visible(False)
ax.axis["yzero"].set_axis_direction("left")
ax.grid(False)
ax.minorticks_on()

x = linspace(.001,3,150)
ax.plot(x,pdf(1.,0.,x))
ax.text(.1,.7,r'$\mu=0$, $\sigma=1$',color='b')

ax.plot(x,pdf(.5,0.,x),'g')
ax.text(.15,.9,r'$\mu=0$, $\sigma=0.5$',color='g')

ax.plot(x,pdf(.25,0.,x),'r')
ax.text(.5,1.7,r'$\mu=0$, $\sigma=0.25$',color='r')

ax.set_ylim(0,2.1)
ax.set_xlim(0,3)

ax.axis["xzero"].label.set_text(r'$x$')
ax.axis["yzero"].label.set_text(r'$f_x(x;\mu,\sigma)=\frac{1}{x\sigma\sqrt{2\pi}}e^{-\frac{\left(\ln x-\mu\right)^2}{2\sigma^2}}$')

fig.savefig("Test.svg",bbox_inches="tight",pad_inches=.15)