expected_var_t = t expected_cov_st = min(s, t) elif which_process == 'bbbm' or which_process == 'bbsde': expected_mean_s = X0 + s / T * (XT - X0) expected_mean_t = X0 + t / T * (XT - X0) expected_var_s = s * (T - s) / T expected_var_t = t * (T - t) / T if s < t: expected_cov_st = s * (T - t) / T else: expected_cov_st = t * (T - s) / T mean_s = stats_m.find_mean(slice_s) mean_t = stats_m.find_mean(slice_t) var_s = stats_m.find_sampvaraux(slice_s, mean_s) var_t = stats_m.find_sampvaraux(slice_t, mean_t) cov_st = stats_m.find_sample_covariance(slice_s, slice_t) diff_mean_s = mean_s - expected_mean_s diff_mean_t = mean_t - expected_mean_t diff_var_s = var_s - expected_var_s diff_var_t = var_t - expected_var_t diff_cov_st = cov_st - expected_cov_st if which_process == 'bm': print 'T = %11.7f' % T elif which_process == 'bbbm' or which_process == 'bbsde': print 'X0 = %11.7f' % X0 print 'XT = %11.7f' % XT print 'T = %11.7f' % T
expected_var_t = t expected_cov_st = min(s, t) elif which_process == 'bbbm' or which_process == 'bbsde': expected_mean_s = X0 + s/T*(XT-X0) expected_mean_t = X0 + t/T*(XT-X0) expected_var_s = s*(T-s)/T expected_var_t = t*(T-t)/T if s < t: expected_cov_st = s*(T-t)/T else: expected_cov_st = t*(T-s)/T mean_s = stats_m.find_mean(slice_s) mean_t = stats_m.find_mean(slice_t) var_s = stats_m.find_sampvaraux(slice_s, mean_s) var_t = stats_m.find_sampvaraux(slice_t, mean_t) cov_st = stats_m.find_sample_covariance(slice_s, slice_t) diff_mean_s = mean_s - expected_mean_s diff_mean_t = mean_t - expected_mean_t diff_var_s = var_s - expected_var_s diff_var_t = var_t - expected_var_t diff_cov_st = cov_st - expected_cov_st if which_process == 'bm': print 'T = %11.7f' % T elif which_process == 'bbbm' or which_process == 'bbsde': print 'X0 = %11.7f' % X0 print 'XT = %11.7f' % XT print 'T = %11.7f' % T
Ybars = [] for rep in range(0, num_sample_reps): X = random_sample_with_replacement(population, n) Xbar = stats_m.find_mean(X) Xbars.append(Xbar) Ybar = 0.0 for i in range(0, k): stratum = strata[i] ni = nis[i] wi = wis[i] Xi = random_sample_with_replacement(stratum, ni) Xibar = stats_m.find_mean(Xi) Ybar += wi * Xibar Ybars.append(Ybar) EXbar = stats_m.find_mean(Xbars) EYbar = stats_m.find_mean(Ybars) VXbar = stats_m.find_sampvaraux(Xbars, true_mu) VYbar = stats_m.find_sampvaraux(Ybars, true_mu) print "n = %7d" % (n) for i in range(0, k): print "n_%d = %7d" % (i, nis[i]) print print "E[Xbar] = %7.4f" % (EXbar) print "E[Ybar] = %7.4f" % (EYbar) print "E[(Xbar-m)^2] = %7.4f" % (VXbar) print "E[(Ybar-m)^2] = %7.4f" % (VYbar)