Bernoulli
Provides an implementation of the Bernoulli distribution with success probability (p) P(X=1) = p P(X=0) = 1-p
Parameters
the probability of success, must be between (0,1)
an optional name
Properties
Functions
Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
Returns an array of probabilities each representing F(x_i). The CDF is evaluated for each point in the input array x and the probabilities are returned in the returned array.
Returns the probability of being in the interval, F(upper limit) - F(lower limit) Be careful, this is Pr{lower limit < = X < = upper limit} which includes the lower limit and has implications if the distribution is discrete
Returns the Pr{x1 <= X <= x2} for the distribution. Be careful, this is Pr{x1 <= X <= x2} which includes the lower limit and has implications if the distribution is discrete
Computes the complementary cumulative probability distribution function for given value of x. This is P{X > x}
Provides the inverse cumulative distribution function for the distribution
Computes x_p where P(X <= x_p) = p for the supplied array of probabilities. Requires that the values within the supplied array are in (0,1)
Gets the parameters
Sets the parameters
If x is not an integer value, then the probability must be zero otherwise pmf(int x) is used to determine the probability
Returns the f(i) where f represents the probability mass function for the distribution.
Computes the probabilities associated with the range and returns the value and the probability as a map with the integer value as the key and the probability as the related value.
Returns the standard deviation for the distribution as the square root of the variance if it exists
Computes Pr{x < X } for the distribution.