indicates whether pmf and cdf calculations are done by recursive (iterative) algorithm based on logarithms or via beta incomplete function and binomial coefficients.

Functions

cdf

open fun cdf(x: DoubleArray): DoubleArray

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.

open fun cdf(interval: Interval): Double

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

open fun cdf(x1: Double, x2: Double): Double

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

open override fun cdf(x: Double): Double

Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function

fun cdf(x: Int): Double

complementaryCDF

open fun complementaryCDF(x: Double): Double

Computes the complementary cumulative probability distribution function for given value of x. This is P{X > x}

firstOrderLossFunction

open override fun firstOrderLossFunction(x: Double): Double

Computes the first order loss function for the function for given value of x, G1(x) = Emax(X-x,0)

instance

open override fun instance(): Poisson

invCDF

open fun invCDF(probabilities: DoubleArray): DoubleArray

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)

open override fun invCDF(p: Double): Double

Provides the inverse cumulative distribution function for the distribution

mean

open override fun mean(): Double

Returns the mean or expected value of a distribution

parameters

open override fun parameters(): DoubleArray

Gets the parameters for the distribution

open override fun parameters(params: DoubleArray)

Sets the parameters for the distribution parameters0 should be the mean rate

pmf

open fun pmf(x: Double): Double

If x is not an integer value, then the probability must be zero otherwise pmf(int x) is used to determine the probability

open fun pmf(range: IntRange): Map<Int, Double>

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.

open override fun pmf(i: Int): Double

Returns the f(i) where f represents the probability mass function for the distribution.

probIn

open override fun probIn(range: IntRange): Double

Computes the sum of the probabilities over the provided range. If the range is closed a..b then the end point b is included in the sum. If the range is open a..<b then the point b is not included in the sum.

randomVariable