.. _docs-meteoinfolab-numeric-stats-beta: ************ beta ************ .. currentmodule:: numeric.stats .. attribute:: beta A beta continuous random variable. Notes ----- The probability density function for beta is: .. math:: f(x, a, b) = \frac{\gamma(a+b) x^{a-1} (1-x)^{b-1}} {\gamma(a) \gamma(b)} for :math:0 < x < 1, :math:a > 0, :math:b > 0, where :math:\gamma(z) is the gamma function. beta takes :math:a and :math:b as shape parameters. Examples:: from mipylib.numeric import stats x = arange(0.01, 1, 0.01) aa = [0.5, 5, 1, 2,2] bb = [0.5, 1, 3, 2 ,5] ss = ['-b', '-r', '-c', '-g', '-m'] #PDF subplot(1,2,1) for a,b,s in zip(aa,bb,ss): y = stats.beta.pdf(x, a, b) plot(x, y, s, label=r'$\alpha = %.1f, \beta = %.1f$' % (a, b)) legend(loc='upper left', facecolor='w') ylim(0, 5) xlim(0, 1) title('PDF') #CDF subplot(1,2,2) for a,b,s in zip(aa,bb,ss): y = stats.beta.cdf(x, a, b) plot(x, y, s, label=r'$\alpha = %.1f, \beta = %.1f$' % (a, b)) legend(loc='lower right', facecolor='w') ylim(0, 1) xlim(0, 1) title('CDF') suptitle('Beta distribution') .. image:: ../../../../_static/beta_distribution.png