Poisson taqsimoti
Poisson taqsimoti
Poisson taqsimoti — diskret taqsimot.
U belgilangan vaqt ichida hodisa necha marta ro‘y berishi mumkinligini baholaydi. Masalan, agar kimdir kuniga ikki marta ovqatlansa, uning uch marta ovqatlanish ehtimolligi qancha?
Uning ikkita parametri bor:
lam — chastota yoki hodisalarning ma’lum soni, masalan, yuqoridagi masala uchun 2.
size — qaytariladigan massivning shakli.
Misol
Hodisalar soni 2 bo‘lgan 1x10 o‘lchamli tasodifiy taqsimot hosil qiling:
from numpy import random
x = random.poisson(lam=2, size=10)
print(x)
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Poisson taqsimotini vizuallashtirish
Misol
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
sns.displot(random.poisson(lam=2, size=1000))
plt.show()
Natija
Normal va Poisson taqsimoti o‘rtasidagi farq
Normal taqsimot uzluksiz, Poisson taqsimoti esa diskret.
Biroq binomial taqsimotdagi kabi, yetarlicha katta Poisson taqsimoti ham ma’lum standart chetlanish va o‘rtacha qiymatga ega normal taqsimotga o‘xshab qolishini ko‘rishimiz mumkin.
Misol
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
data = {
"normal": random.normal(loc=50, scale=7, size=1000),
"poisson": random.poisson(lam=50, size=1000)
}
sns.displot(data, kind="kde")
plt.show()
Natija
Binomial va Poisson taqsimoti o‘rtasidagi farq
Binomial taqsimotda faqat ikkita mumkin bo‘lgan natija bor, Poisson taqsimotida esa mumkin bo‘lgan natijalar soni cheksiz bo‘lishi mumkin.
Biroq juda katta n va nolga yaqin p qiymatlarida binomial taqsimot Poisson taqsimotiga deyarli bir xil bo‘ladi, bunda n * p taxminan lamga teng bo‘ladi.
Misol
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
data = {
"binomial": random.binomial(n=1000, p=0.01, size=1000),
"poisson": random.poisson(lam=10, size=1000)
}
sns.displot(data, kind="kde")
plt.show()
Natija
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