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EmJ
EmJ

Reputation: 4608

How to calculate the poisson random variable probability in scipy?

I want to calculate sum(e-λ λi/i!) where i=197,..., ∞ and λ=421.41 using scipy.

I went through the scipy documentation of scipy.stats.poisson which can be found in https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html

However, they have multiple methods for scipy.stats.poisson and bit confused in picking the method that suits me most.

e.g.,

rvs(mu, loc=0, size=1, random_state=None)   Random variates.
pmf(k, mu, loc=0)   Probability mass function.
logpmf(k, mu, loc=0)    Log of the probability mass function.
cdf(k, mu, loc=0)   Cumulative distribution function.
logcdf(k, mu, loc=0)    Log of the cumulative distribution function.
sf(k, mu, loc=0)    Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).
logsf(k, mu, loc=0) Log of the survival function.
ppf(q, mu, loc=0)   Percent point function (inverse of cdf — percentiles).
isf(q, mu, loc=0)   Inverse survival function (inverse of sf).
stats(mu, loc=0, moments=’mv’)  Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(mu, loc=0)  (Differential) entropy of the RV.
expect(func, args=(mu,), loc=0, lb=None, ub=None, conditional=False)    Expected value of a function (of one argument) with respect to the distribution.
median(mu, loc=0)   Median of the distribution.
mean(mu, loc=0) Mean of the distribution.
var(mu, loc=0)  Variance of the distribution.
std(mu, loc=0)  Standard deviation of the distribution.
interval(alpha, mu, loc=0)  Endpoints of the range that contains alpha percent of the distribution

Currently, I am using sf(197, 421.41, loc=0). However, I am not very sure if I have picked the right method. Please let me know your thoughts.

I am happy to provide more details if needed.

Upvotes: 0

Views: 1750

Answers (1)

Tarifazo
Tarifazo

Reputation: 4343

The exponential factor (e-λ λi/i!) is the probability density (mass) function of the poisson distribution, while the sum is the cumulative probability (distribution) function. Methods correspond to .pmf and .cdf respectively.

Example:

from scipy.stats import poisson
k, mu = 1, 2
print(poisson.pmf(k, mu))   #k, mu
print(np.exp(-mu) * mu**k / np.math.factorial(k))
print(poisson.cdf(k, mu))
print(sum(np.exp(-mu) * mu**j / np.math.factorial(j) for j in range(k + 1)))

>>0.2706705664732254
0.2706705664732254
0.40600584970983794
0.4060058497098381

In your case:

k, mu = 197, 421.41
print(1 - poisson.cdf(k - 1, mu))

Note that it will give 1.0 due to numerical precision

Upvotes: 1

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