KSLCore/ksl.utilities.distributions/Geometric

Geometric

class Geometric(successProb: Double = 0.5, name: String? = null) : Distribution, DiscretePMFInRangeDistributionIfc, LossFunctionDistributionIfc, GetRVariableIfc, RVParametersTypeIfc

The geometric distribution is the probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... }, where X is the number of Bernoulli trials needed to get one success.

Parameters

successProb

the probability of success

name

an optional label/name

Constructors

Geometric

constructor(parameters: DoubleArray)

Constructs a Geometric using the supplied parameters array parameters0 is probability of success

constructor(successProb: Double = 0.5, name: String? = null)

Types

Companion

object Companion

Properties

open override val id: Int

label

open override var label: String?

name

open override val name: String

parametrizedRVClass

open override val parametrizedRVClass: KClass<out ParameterizedRV>

pFailure

val pFailure: Double

The probability of failure on a trial

pSuccess

var pSuccess: Double

The probability of success on a trial

randomVariable

open val randomVariable: RVariableIfc

rvParameters

open override val rvParameters: RVParameters

the parameters for this type of random variable

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

computes the cdf of the distribution F(X<=x)

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(): Geometric

invCDF

open override fun invCDF(p: Double): Double

Gets the inverse cdf for the distribution

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)

mean

open override fun mean(): Double

Returns the mean or expected value of a distribution

parameters

open override fun parameters(): DoubleArray

Gets the parameters as an array parameters0 is probability of success

open override fun parameters(params: DoubleArray)

Sets the parameters using the supplied array parameters0 is probability of success

pmf

open override fun pmf(i: Int): Double

computes the pmf of the distribution f(x) = p(1-p)^(x) for x>=0, 0 otherwise

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.

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

open override fun randomVariable(stream: RNStreamIfc): RVariableIfc

open fun randomVariable(streamNum: Int): RVariableIfc

secondOrderLossFunction

open override fun secondOrderLossFunction(x: Double): Double

Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)Emax(X-x,0)*max(X-x-1,0)

standardDeviation

open fun standardDeviation(): Double

Returns the standard deviation for the distribution as the square root of the variance if it exists

strictlyLessCDF

open fun strictlyLessCDF(x: Double): Double

Computes Pr{x < X } for the distribution.

toString

open override fun toString(): String

variance

open override fun variance(): Double

Returns the variance of the distribution if defined