Sports Analyst Meetup #5 LT発表 「確率分布の成り立ちを理解してスポーツにあてはめてみる」

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5. Univariate Distribution Relationships
Lawrence M. LEEMIS and Jacquelyn T. MCQUESTON
http://www.math.wm.edu/~leemis/2008amstat.pdf

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9. #
#
p = 0.7
trial_size = 10000
rd.seed(71) #
data = st.bernoulli.rvs(p, size=trial_size)
#
#
p = 0.7
trial_size = 10000
rd.seed(71)
#
data = st.bernoulli.rvs(p, size=trial_size)
h = plt.hist(data, normed=True, color=red, label="rvs", alpha=0.8)
width = np.diff(h[1]).mean()
#
plt.bar([0.1, 0.9], [(1-p)/width, p/width], width=width, color="b", label="Theoretical", alpha=0.8)
plt.legend(loc="best")
plt.show()

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12. #
def gen_bern_var(p, n):
return(np.sum(st.bernoulli.rvs(p, size=n)))
#
p = 0.7
trial_size = 100000
set_size = 30
rd.seed(71)
result = [gen_bern_var(p, set_size) for _
in range(trial_size)]
hist_range = np.arange(np.min(result), np.max(result)+1)
xx = np.arange(0, set_size)
plt.figure(figsize=(10,6))
h = plt.hist(result, normed=True, bins=hist_range, color=red, label="rvs")
plt.bar(xx+0.5, st.binom.pmf(xx, n=set_size, p=p), width=1, alpha=0.5, label="Theoretical")
plt.legend(loc="best") plt.title(f"binomial distribution trial_size={trial_size},
set_size:{set_size}, p:{p}")
plt.show()
n_success: 4655, trial_size:100000
empirical:0.04655, theoretical:0.04644

13. https://www.kaggle.com/kenmatsu4/basket-shot-log-binom
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https://www.kaggle.com/dansbecker/nba-shot-logs

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17. https://www.kaggle.com/kenmatsu4/basket-shot-log-poisson
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18. https://www.kaggle.com/dansbecker/nba-shot-logs

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21. #
set_size = 20000 ; p = 0.1
trial_size = 50000
result = [gen_bern_var(p, set_size)
for _ in range(trial_size)]
xx = np.arange(np.percentile(result, 0.01),
np.percentile(result, 99.99))
# confidence interval
ci = st.norm.interval(0.95, loc=set_size*p,
scale=np.sqrt(set_size*p*(1-p)))
print(f"lower:{ci[0]}, upper:{ci[1]}")
plt.figure(figsize=(10,6))
plt.plot(xx, st.norm.pdf(xx, set_size*p, np.sqrt(set_size*p*(1-p))),
alpha=0.8, label="Theoretical")
plt.hist(result, normed=True, bins=30, color=red, label="rvs", alpha=0.7)
plt.title(f"normal distribution trial_size={trial_size}, set_size:{set_size}, p:{p}")
plt.legend(loc="best")
plt.show()
0.95 confidence interval
lower:1916.8
upper:2083.2

22. https://www.slideshare.net/matsukenbook/rev012
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27. EOF