import numpy as np
import scipy.stats
import matplotlib.pyplot as plt 

maxx = 8.0
rc('text.latex', preamble='\usepackage{sfmath}')
rc('text', usetex=True)
rc('font', family='sans-serif')

x = np.arange(0,maxx,0.01)
rayl = scipy.stats.rayleigh(loc=0,scale=2)
p = rayl.pdf(x)
x67 = rayl.ppf(2/3.0)
idx0_67 = x < x67
maxidx = np.max(np.where(idx0_67)[0])
idx67_0 = x >= x67
idx67_0[maxidx] = True


fig = plt.figure(figsize=(10,4))
ax = fig.add_axes([0,0,1,1],frameon=True)
ax.set_ylim(0,0.48)

ax.set_xlim(0, maxx)
ax.fill_between(x[idx0_67],np.zeros(p.shape)[idx0_67], p[idx0_67], alpha=0.5, color=(0.2,0.4,0.8))
ax.fill_between(x[idx67_0],np.zeros(p.shape)[idx67_0], p[idx67_0], alpha=0.5, color=(0.2,0.6,0.8))
ax.vlines(x67, 0, rayl.pdf(x67), linewidth=2, alpha=0.5)
ax.vlines(rayl.kwds['scale'], 0, rayl.pdf(rayl.kwds['scale']), linewidth=2, alpha=0.5)
ax.annotate("mode",
            xy=(rayl.kwds['scale'], rayl.pdf(rayl.kwds['scale'])), xycoords='data',
            xytext=(100, 50), textcoords='offset points',
            va="bottom", ha="left",
            arrowprops=dict(arrowstyle="->",
                            connectionstyle="arc3,rad=0.2",
                             mutation_scale=15,
                             linewidth=2,
                             edgecolor='black'
                            ), 
            fontsize='large')

ax.vlines(rayl.median(), 0, rayl.pdf(rayl.median()), linewidth=2, alpha=0.5)
ax.annotate("median",
            xy=(rayl.median(), rayl.pdf(rayl.median())), xycoords='data',
            xytext=(100, 30), textcoords='offset points',
            va="bottom", ha="left",
            arrowprops=dict(arrowstyle="->",
                            connectionstyle="arc3,rad=0.2",
                             mutation_scale=15,
                             linewidth=2,
                             edgecolor='black'
                            ), 
            fontsize='large')
ax.vlines(rayl.mean(), 0, rayl.pdf(rayl.mean()), linewidth=2, alpha=0.5)
ax.annotate(r"mean, $\bar{H}$",
            xy=(rayl.mean(), rayl.pdf(rayl.mean())), xycoords='data',
            xytext=(100, 10), textcoords='offset points',
            va="bottom", ha="left",
            arrowprops=dict(arrowstyle="->",
                            connectionstyle="arc3,rad=0.2",
                             mutation_scale=15,
                             linewidth=2,
                             edgecolor='black'
                            ), 
            fontsize='large')
ax.vlines(rayl.ppf(5/6.0), 0, rayl.pdf(rayl.ppf(5/6.0)), linewidth=2, alpha=0.5)
ax.annotate("significant wave height, $H_{S}$",
            xy=(rayl.ppf(5/6.0), rayl.pdf(rayl.ppf(5/6.0))), xycoords='data',
            xytext=(100, 30), textcoords='offset points',
            va="bottom", ha="left",
            arrowprops=dict(arrowstyle="->",
                            connectionstyle="arc3,rad=0.2",
                             mutation_scale=15,
                             linewidth=2,
                             edgecolor='black'
                            ), 
            fontsize='large')
ax.vlines(rayl.ppf(9/10.0), 0, rayl.pdf(rayl.ppf(9/10.0)), linewidth=2, alpha=0.5)
ax.annotate("90th percentile, $H_{1/10}$",
            xy=(rayl.ppf(9/10.0), rayl.pdf(rayl.ppf(9/10.0))), xycoords='data',
            xytext=(100, 30), textcoords='offset points',
            va="bottom", ha="left",
            arrowprops=dict(arrowstyle="->",
                            connectionstyle="arc3,rad=0.2",
                             mutation_scale=15,
                             linewidth=2,
                             edgecolor='black'
                            ), 
            fontsize='large')

center = (maxx+rayl.ppf(2/3.0))/2.0+1
ax.text(center, 0.04, '1/3 of waves', ha='center', va='center', fontsize='large')
arrow = matplotlib.patches.FancyArrowPatch(
    posA=(rayl.ppf(4/6.0), 0.04), posB=(center, 0.04), arrowstyle='<-',
    mutation_scale=15.0, linewidth=2, edgecolor='black',
    shrinkB=50
    )
ax.add_patch(arrow)
arrow = matplotlib.patches.FancyArrowPatch(
    posA=(center, 0.04), posB=(maxx, 0.04), arrowstyle='->',
    mutation_scale=15.0, linewidth=2, edgecolor='black',
    shrinkA=50
    )
ax.add_patch(arrow)
ax.set_xlabel('wave height', size='x-large')
ax.set_xticks([])
ax.set_ylabel('number of waves',size='x-large')
ax.set_yticks([])
ax.set_title('Statistical wave distribution')