PWCEmpirical
Represents a piecewise constant empirical cumulative distribution function (CDF).
This class defines a distribution based on breakpoints and proportions, where the breakpoints represent partitioned intervals of the distribution and the proportions define the probability mass assigned to each corresponding interval.
Parameters
Array of doubles representing the breakpoints. The array must be sorted and values must be finite. There must be at least two breakpoints, and the values must strictly increase. These define the boundaries of the distribution's intervals.
Optional array of proportions corresponding to each interval between breakpoints. The array size should be one less than the size of the breakPoints array. By default, all intervals are assigned equal portions of probability. The proportions must form a valid probability distribution and be in the range (0,1).
Optional name for the distribution, defaulting to null if not provided.
Throws
If the input parameters do not adhere to the necessary constraints (e.g., invalid proportions, breakpoints not sorted, etc.).
Constructors
Creates an instance of PWCEmpiricalCDF.
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}
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)
Provides the inverse cumulative distribution function for the distribution
Assuming that the observations in the array data are from a random sample, this function computes the likelihood function. This is computed using as the sum of the log-likelihood function raised to e. Implementation may want to specify other computationally efficient formulas for this function or (most likely) the sum of the log-likelihood function.
Computes the natural log of the pdf function evaluated at x. Implementations may want to specify computationally efficient formulas for this function.
n = number of break points k = number of proportions k = n - 1 param0 = n param1..n param(n+1)..(n+1+k)
Promises to return a random variable that uses the supplied stream number using the supplied stream provider
Returns the standard deviation for the distribution as the square root of the variance if it exists
Computes the sum of the log-likelihood function evaluated at each observation in the data. Implementations may want to specify computationally efficient formulas for this function.