DEmpirical
Provides a representation for a discrete distribution with arbitrary values and assigned probabilities to each value. Allows the specification of the distribution via a pair of arrays containing the values = {v1, v2, ... , vn} and the cumulative probabilities cdf = {c1, c2, ... , 1.0}
where if p1 is the probability associated with v1, p2 with v2, etc. then c1 = p1, c2 = p1 + p2, c3 = p1 + p2 + p3, etc, with cn = 1.0 (the sum of all the probabilities). If cn is not 1.0, then an exception is thrown.
Parameters
an array of values that will be drawn from, must have distinct values
a cdf corresponding to the values
an optional name/label
Properties
Functions
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
Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
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 for the distribution as an array of paired parameters (value, cumulative probability), Eg. X[] = v1, cp1, v2, cp2, ..., vn, cpn,
Sets the parameters for the distribution. Array of probability points (value, cumulative probability), Eg. X[] = v1, cp1, v2, cp2, ..., vn, cpn, as the input parameters.
The probability mass function for this discrete distribution. Returns the same as pdf.
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.