def __init__(self, the_lambda):
"""
Sets the parameters for the Poisson distribution.
the_lambda must be > 0
"""
if the_lambda <= 0:
raise IncorrectDistributionInicializationError()
self.the_lambda = the_lambda
self.mean = the_lambda
self.variance = the_lambda
self.median = functions.floor_function(the_lambda+1/3-0.02/the_lambda)
self.mode = functions.floor_function(the_lambda)
self.skewness = math.pow(the_lambda, -0.5)
self.ex_kurtosis = math.pow(the_lambda, -1)
def poisson_cdf(k, the_lambda):
"""
Gives the value of the Poisson cumulative density function
for the given k (k can be a whole, nonnrgative nuber)
and the specified parameter of the Poisson distribution-
the_lambda must be > 0.
"""
if the_lambda <= 0:
raise IncorrectInputError()
A = math.exp(-the_lambda)
index = functions.floor_function(k)
summation = 0
for i in range(index+1):
summation += math.pow(the_lambda, i)/functions.factorial(i)
return A*summation
