def test_hypergeometric_range(self):
# Test for ticket #921
assert_(np.all(random.hypergeometric(3, 18, 11, size=10) < 4))
assert_(np.all(random.hypergeometric(18, 3, 11, size=10) > 0))
# Test for ticket #5623
args = [
(2**20 - 2, 2**20 - 2, 2**20 - 2), # Check for 32-bit systems
]
is_64bits = sys.maxsize > 2**32
if is_64bits and sys.platform != 'win32':
# Check for 64-bit systems
args.append((2**40 - 2, 2**40 - 2, 2**40 - 2))
for arg in args:
assert_(random.hypergeometric(*arg) > 0)
def hypergeometric(self, ngood, nbad, nall):
'''Parameters:\n
ngood: integer, >=0.\n
nbad: integer, >=0.\n
nall: integer, >=1 and <=ngood+nbad.
'''
return r.hypergeometric(ngood, nbad, nall, self.size)
def hypothesisTest(self, seq1, seq2, totalSeq1, totalSeq2):
replicates = 10000
# observed difference
obsDiff = float(seq1) / totalSeq1 - float(seq2) / totalSeq2
# randomly permute assignment of sequences
permutationDiffs = []
posSeq = seq1 + seq2
negSeq = totalSeq1 + totalSeq2 - posSeq
for dummy in xrange(0, replicates):
c1 = hypergeometric(posSeq, negSeq, totalSeq1)
c2 = posSeq - c1
permutationDiffs.append(
float(c1) / totalSeq1 - float(c2) / totalSeq2)
# find p-value of permutation test (number of replicates with a value lower/greater than the observed value)
leftCount = 0
rightCount = 0
twoSidedCount = 0
for value in permutationDiffs:
if value <= obsDiff:
leftCount += 1
if value >= obsDiff:
rightCount += 1
if abs(value) >= abs(obsDiff):
twoSidedCount += 1
oneSidedCount = leftCount
if rightCount < oneSidedCount:
oneSidedCount = rightCount
return float(oneSidedCount) / replicates, float(
twoSidedCount) / replicates
def hypothesisTest(self, seq1, seq2, totalSeq1, totalSeq2):
replicates = self.preferences['Replicates']
# observed difference
obsDiff = float(seq1) / totalSeq1 - float(seq2) / totalSeq2
# randomly permute assignment of sequences
permutationDiffs = []
posSeq = seq1+seq2
negSeq = totalSeq1+totalSeq2-posSeq
for dummy in xrange(0, replicates):
c1 = hypergeometric(posSeq, negSeq, totalSeq1)
c2 = posSeq - c1
permutationDiffs.append(float(c1) / totalSeq1 - float(c2) / totalSeq2)
# find p-value of permutation test (number of replicates with a value lower/greater than the observed value)
leftCount = 0
rightCount = 0
twoSidedCount = 0
for value in permutationDiffs:
if value <= obsDiff:
leftCount += 1
if value >= obsDiff:
rightCount += 1
if abs(value) >= abs(obsDiff):
twoSidedCount += 1
oneSidedCount = leftCount
if rightCount < oneSidedCount:
oneSidedCount = rightCount
return float(oneSidedCount) / replicates, float(twoSidedCount) / replicates, ''
def getCardDrawnProbabilities(self, tries=100000):
"""
Calculates, for each card, the probabilities for drawing that card at
least once by each turn up to 10.
The probabilities will be returned as a dict card names and lists
in which each of the indexes of the list tells the probability for
the index-turn.
"""
cardDrawnProbabilities = {}
cardCounts = defaultdict(int)
for card in self._cards:
cardCounts[card.name] += 1
for card in self._cards:
cardDrawnProbabilities[card.name] = []
nGood = cardCounts[card.name]
samples = len(self._cards)
nBad = samples - nGood
for turnNumber in range(0, 11):
#------------------------------------
#The probability for getting AT LEAST one pointed card from
#a sample of total number of cards with a certain number
#of cards drawn can be extracted from the hypergeometric
#distribution.
cardsDrawn = turnNumber + 7
draws = hypergeometric(nGood, nBad, cardsDrawn, tries)
probability = sum(draws >= 1) / float(tries)
cardDrawnProbabilities[card.name].append(probability)
def generate_random_table(rowsums, colsums, dim=[2,2]):
from numpy.random import hypergeometric
#from numpy import array
n11= hypergeometric(rowsums[0], rowsums[1], colsums[0], size=1)[0]
n21= colsums[0] -n11
n12 = rowsums[0]-n11
n22 = rowsums[1]-n21
#table =array([[n11, n21],[ n12, n22]])
return n11,n12,n21,n22
def draw(self):
if self.number_of_cards == 0:
return None
return ExpansionCards(name=ADVENTURES,
kingdom_cards=sorted(random.sample(self.kingdom_cards, self.number_of_cards)),
event_cards=sorted(random.sample(self.event_cards,
min(hypergeometric(len(event_cards),
len(kingdom_cards) + len(event_cards),
self.number_of_cards),
2))))
def _rvs(self, M, n, N):
return mtrand.hypergeometric(n, M - n, N, size=self._size)
def _rvs(self, M, n, N):
return mtrand.hypergeometric(n, M-n, N, size=self._size)
all_doubleton_opportunities[idxs]).astype(
numpy.int32)
low_ngood = low_doubletons.astype(numpy.int32)
low_nbad = (low_doubleton_opportunities - low_doubletons).astype(
numpy.int32)
low_p = low_doubletons.sum() * 1.0 / low_doubleton_opportunities.sum()
all_ngood = all_doubletons[idxs].astype(numpy.int32)
all_nbad = (all_doubleton_opportunities[idxs] - all_ngood).astype(
numpy.int32)
all_p = all_doubletons.sum() * 1.0 / all_doubleton_opportunities.sum()
bootstrapped_low_ps.extend(
hypergeometric(low_ngood, low_nbad, sample_sizes) * 1.0 / sample_sizes)
bootstrapped_all_ps.extend(
hypergeometric(all_ngood, all_nbad, sample_sizes) * 1.0 / sample_sizes)
bootstrapped_fake_low_ps.extend(
binomial(sample_sizes, low_p) * 1.0 / sample_sizes)
bootstrapped_fake_all_ps.extend(
binomial(sample_sizes, all_p) * 1.0 / sample_sizes)
#xs, ns = stats_utils.calculate_unnormalized_survival_from_vector(bootstrapped_low_ps, min_x=0,max_x=2)
#sharing_axis.step(xs,ns*1.0/ns[0],'r-',label='Low $d_S$ (matched)',zorder=3)
#xs, ns = stats_utils.calculate_unnormalized_survival_from_vector(bootstrapped_all_ps, min_x=0,max_x=2)
#sharing_axis.step(xs,ns*1.0/ns[0],'k-',label='All (matched)',zorder=2)
#xs, ns = stats_utils.calculate_unnormalized_survival_from_vector(bootstrapped_fake_low_ps, min_x=0,max_x=1)
#sharing_axis.step(xs,ns*1.0/ns[0],'r-',label='Low $d_S$ (pooled)',zorder=1,alpha=0.5)
#print(a)
print("計算結果:",total1/10000)
total2=total1/10000
plt.hist(total,bins=5)
plt.axvline(x=0.2617,ymin=0,ymax=10,c='red')
plt.axvline(x=total2,ymin=0,ymax=10,c='black')
plt.show()
print()
print("-----------------超幾何分配")
import numpy.random as nr
all=[]
total=0 # 這個問題機率是 0.3687
for i in range(1000): # 1000 次大實驗，共有 1000x100 個數據
s=nr.hypergeometric(20,15,5,100) # 總人數 :35，男:20、女:15，隨機抽五人，裏頭的男生數
#print('樣本為5個,5個裡面男生的數量:')
#print(s)
p=sum(s==3)/100 # 恰好男生數是 3 的組數再做平均
total+=p # 1000 次平均的總和
all.append(p) # 每次平均都存進 all，共 1000 次
print(total/1000) # 100000 個中恰好男生數是 3 的數據平均
x=np.arange(1000)
plt.hist(all,bins=10)
plt.axvline(x=total/1000,ymin=0,ymax=1,c='red')
plt.show()
print()
print("-----------------常態分配")
x=np.random.normal(5,1,8) # normal(平均值,標準差,size)
y=np.random.normal(5,2,8)
# resampe everything at known rates
idxs = choice(numpy.arange(0,len(all_doubletons)),size=len(low_doubletons))
sample_sizes = numpy.fmin(low_doubleton_opportunities, all_doubleton_opportunities[idxs]).astype(numpy.int32)
low_ngood = low_doubletons.astype(numpy.int32)
low_nbad = (low_doubleton_opportunities-low_doubletons).astype(numpy.int32)
low_p = low_doubletons.sum()*1.0/low_doubleton_opportunities.sum()
all_ngood = all_doubletons[idxs].astype(numpy.int32)
all_nbad = (all_doubleton_opportunities[idxs] - all_ngood).astype(numpy.int32)
all_p = all_doubletons.sum()*1.0/all_doubleton_opportunities.sum()
bootstrapped_low_ps.extend( hypergeometric(low_ngood, low_nbad, sample_sizes)*1.0/sample_sizes )
bootstrapped_all_ps.extend( hypergeometric(all_ngood, all_nbad, sample_sizes)*1.0/sample_sizes )
bootstrapped_fake_low_ps.extend( binomial(sample_sizes, low_p)*1.0/sample_sizes )
bootstrapped_fake_all_ps.extend( binomial(sample_sizes, all_p)*1.0/sample_sizes )
#xs, ns = stats_utils.calculate_unnormalized_survival_from_vector(bootstrapped_low_ps, min_x=0,max_x=2)
#sharing_axis.step(xs,ns*1.0/ns[0],'r-',label='Low $d_S$ (matched)',zorder=3)
#xs, ns = stats_utils.calculate_unnormalized_survival_from_vector(bootstrapped_all_ps, min_x=0,max_x=2)
#sharing_axis.step(xs,ns*1.0/ns[0],'k-',label='All (matched)',zorder=2)
#xs, ns = stats_utils.calculate_unnormalized_survival_from_vector(bootstrapped_fake_low_ps, min_x=0,max_x=1)
#sharing_axis.step(xs,ns*1.0/ns[0],'r-',label='Low $d_S$ (pooled)',zorder=1,alpha=0.5)
def hypergeometric(size, params):
try:
return random.hypergeometric(params['ngood'], params['nbad'],
params['nsample'], size)
except ValueError as e:
exit(e)