def __init__(self, y: float):
super().__init__(samplespace=R((0, inf)))
assert y > 0, Exception
self.y = y
def rvsvar(self, P: float, n: int = None, p: float = None) -> 'Binomial':
# Almost one parameter need to be specified
assert (n is not None or p is not None) and P in R((0, 1)), Exception
# Given Var(X) and n, return Binomial with parameter p
if p is None: return Binomial(n, (1 + (1 - (4 * (P / n)))**0.5) / 2)
# Given Var(X) and p, return Binomial with parameter n
return Binomial(P / (p * (1 - p)), p)
def rvsev(self, P: float, n: int = None, p: float = None) -> 'Binomial':
# Almost one parameter need to be defined
assert (n is not None or p is not None) and P in R((0, 1)), Exception
# Given E(X) and n, return new Binomial with parameter p
if p is None: return Binomial(n, P / n)
# Given E(X) and p, return new Binomial with parameter n
return Binomial(P / p, p)
def rvspmf(self, x: int, n: int, P: float) -> 'Binomial':
# Verify integrity of parameters
assert x in N([0, ..., inf]) and n in N([0, ..., inf]) and P in R((0, 1))
# The equation to which to apply the zero theorem
f = lambda c: (comb(n, x) * c**x * (1 - c)**(n - x)) - P
# Given pmf(x) = P, return Binomial with parameter n and p
return Binomial(n, R.bfzero(f, (0, 1)))
def __init__(self, p):
# Call super class with a list of possible specifications (infinite, numerative specifications)
super().__init__(samplespace=N())
assert p in R([0,1]), Exception
# Probability parameter p of success of bernoulli event
self.p = p
def __init__(self, mu, sigma):
super().__init__(samplespace=R((-inf, inf)))
# Mean
self.mu = mu
# teta ∈ R+
assert sigma >= 0, Exception()
# Standard deviation
self.sigma = sigma
def __init__(self, n: int = 0, p: float = 0):
# Call super class with list of specifications
super().__init__(samplespace=N([0, ..., n]))
# p need to be in (0,1) and n must be natural value
assert p in R([0, 1]) and n in N()
# Probability parameter p of success of bernoulli event
self.p = p
# Number of independents events
self.n = n
def quantile(data, q):
assert data is not None and q in R((0,1)), Exception
# Riordino l'array
data = sorted(data)
s,e = (ceil(len(data)*q), len(data) - floor(len(data)*(1-q)))
# Interpolazione
return (lambda s,e: (s*q + e*(1-q)))(*data[s-1: e+1])
def __init__(self, a, b):
super().__init__(samplespace=R((a, b)))
def rvsdevstd(P: float) -> 'Bernoulli':
# Verify integrity of value d passed
assert P in R((0, 1)), Exception
# p = (1 + (1 - (4*var)**0.5)) / 2)) ** 0.5
return Bernoulli(rvsvar(P**2))
def rvsvar(P):
# Variance need to be in (0,1)
assert P in R((0, 1)), Exception
# p = 1 + (1 - (4*var)**0.5)) / 2)
return Bernoulli((1 + (1 - (4 * P))**0.5) / 2)
def rvsev(P):
# Excpected value need to be in (0,1)
assert P in R((0, 1)), Exception
# p = ev
return Bernoulli(P)
def rvspmf(x: int, P: float):
# Verify integrity of parameters
assert x in N([0, ..., inf]) and P in R((0, 1))
# p =
return Bernoulli(P if x == 0 else 1 - P)
def rvsdevstd(self, P: float):
# Verify integrity of value d passed
assert P in R((0, 1)), Exception
# Given DevStd(X), return new Binomial with parameter p or n
return self.fvar(P**2)