def example_n(): print skewnorm.pdf(1,0), stats.norm.pdf(1), skewnorm.pdf(1,0) - stats.norm.pdf(1) print skewnorm.pdf(1,1000), stats.chi.pdf(1,1), skewnorm.pdf(1,1000) - stats.chi.pdf(1,1) print skewnorm.pdf(-1,-1000), stats.chi.pdf(1,1), skewnorm.pdf(-1,-1000) - stats.chi.pdf(1,1) rvs = skewnorm.rvs(0,size=500) print 'sample mean var: ', rvs.mean(), rvs.var() print 'theoretical mean var', skewnorm.stats(0) rvs = skewnorm.rvs(5,size=500) print 'sample mean var: ', rvs.mean(), rvs.var() print 'theoretical mean var', skewnorm.stats(5) print skewnorm.cdf(1,0), stats.norm.cdf(1), skewnorm.cdf(1,0) - stats.norm.cdf(1) print skewnorm.cdf(1,1000), stats.chi.cdf(1,1), skewnorm.cdf(1,1000) - stats.chi.cdf(1,1) print skewnorm.sf(0.05,1000), stats.chi.sf(0.05,1), skewnorm.sf(0.05,1000) - stats.chi.sf(0.05,1)
def examples_normexpand(): skewnorm = SkewNorm_gen() rvs = skewnorm.rvs(5, size=100) normexpan = NormExpan_gen(rvs, mode='sample') smvsk = stats.describe(rvs)[2:] print('sample: mu,sig,sk,kur') print(smvsk) dmvsk = normexpan.stats(moments='mvsk') print('normexpan: mu,sig,sk,kur') print(dmvsk) print('mvsk diff distribution - sample') print(np.array(dmvsk) - np.array(smvsk)) print('normexpan attributes mvsk') print(mc2mvsk(normexpan.cnt)) print(normexpan.mvsk) mnc = mvsk2mnc(dmvsk) mc = mnc2mc(mnc) print('central moments') print(mc) print('non-central moments') print(mnc) pdffn = pdf_moments(mc) print('\npdf approximation from moments') print('pdf at', mc[0] - 1, mc[0] + 1) print(pdffn([mc[0] - 1, mc[0] + 1])) print(normexpan.pdf([mc[0] - 1, mc[0] + 1]))
def examples_normexpand(): skewnorm = SkewNorm_gen() rvs = skewnorm.rvs(5,size=100) normexpan = NormExpan_gen(rvs, mode='sample') smvsk = stats.describe(rvs)[2:] print 'sample: mu,sig,sk,kur' print smvsk dmvsk = normexpan.stats(moments='mvsk') print 'normexpan: mu,sig,sk,kur' print dmvsk print 'mvsk diff distribution - sample' print np.array(dmvsk) - np.array(smvsk) print 'normexpan attributes mvsk' print mc2mvsk(normexpan.cnt) print normexpan.mvsk mnc = mvsk2mnc(dmvsk) mc = mnc2mc(mnc) print 'central moments' print mc print 'non-central moments' print mnc pdffn = pdf_moments(mc) print '\npdf approximation from moments' print 'pdf at', mc[0]-1,mc[0]+1 print pdffn([mc[0]-1,mc[0]+1]) print normexpan.pdf([mc[0]-1,mc[0]+1])