def binomial_plot(p, n):
x_ax = [k for k in range(n)]
y_ax = [dist.binomial_pdf(p, k, n) for k in range(n)] # poisson distribution
mp = pu.PlotUtilities("Binomial Distribution for p={0}".format(p), "# Successes", "Probability")
mp.multiPlot(x_ax, [y_ax], 'o')
def pdf(self, z):
p_z = conditional_default_prob(self.rho, self.p, z)
if self.usePoissonApprox:
return dist.poisson_pdf(self.N * p_z, self.k)
else:
return dist.binomial_pdf(p_z, self.k, self.N)
def comparison_poi_binom(lam, upper_bound):
n = upper_bound + 1
x_ax = [k for k in range(n)]
n_plots = 2 # plotting both poisson and binomial distribution
y_ax = [0.] * n_plots
y_ax[0] = [dist.poisson_pdf(lam, k) for k in range(n)] # poisson distribution
y_ax[1] = [dist.binomial_pdf(lam / n, k, n) for k in range(n)]
mp = pu.PlotUtilities("Poisson Vs Binomial distribution for lambda={0}".format(lam), "# Successes", "Probability")
mp.multiPlot(x_ax, y_ax, '*')
def conditional_binomial_prob(k, N, rho, p, z):
p_z = conditional_default_prob(rho, p, z)
return (dist.binomial_pdf(p_z, k, N))