%matplotlib inline
pyplot.style.use(config.glyfish_style)
# %%
k = 5.0
λ = 1.0
nsample = 50000
samples = numpy.random.weibull(k, nsample)
# %%
target_pdf = stats.weibull(k, λ)
x = numpy.linspace(0.001, 2.0, 500)
figure, axis = pyplot.subplots(figsize=(12, 5))
axis.set_xlabel("X")
axis.set_ylabel("PDF")
axis.set_xlim([0.0, x[-1]])
axis.set_title(f"Weibull Distribution, k={k}, λ={λ}")
axis.plot(x, [target_pdf(j) for j in x])
# %%
figure, axis = pyplot.subplots(figsize=(12, 5))
axis.set_xlabel("Sample")
axis.set_ylabel("PDF")
axis.set_title(f"Weibull Distribution, k={k}, λ={λ}")
axis.set_xlabel(r"$X$")
axis.set_title("Sampled Exponential Distribution")
axis.set_prop_cycle(config.distribution_sample_cycler)
axis.hist(samples, 60, density=True, rwidth=0.8, label=f"Samples", zorder=5)
axis.plot(x, pdf(x), label=f"Target PDF", zorder=6, color="#003B6F")
axis.legend(bbox_to_anchor=(0.9, 0.8))
config.save_post_asset(figure, "inverse_cdf_sampling", "exponetial_sampled_distribution")
# %%
# Inverse CDF sampling from weibull distribution
k = 5.0
λ = 1.0
nsamples = 100000
pdf = stats.weibull(k, λ)
cdf_inv = lambda u: λ * (numpy.log(1.0/(1.0 - u)))**(1.0/k)
x = numpy.linspace(0.001, 1.6, 500)
dx = 1.6/499.0
samples = [cdf_inv(u) for u in numpy.random.rand(nsamples)]
# %%
figure, axis = pyplot.subplots(figsize=(10, 6))
axis.set_ylim([0, 2.0])
axis.set_xlabel(r"$X$")
axis.set_xlim([0.0, 1.6])
axis.set_yticks([0.2, 0.6, 1.0, 1.4, 1.8])
axis.set_title(f"Weibull Distribution, k={k}, λ={λ}")
pdf_values = [pdf(v) for v in x]