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])
