Triangular

class Triangular(theMin: Double = 0.0, theMode: Double = 0.0, theMax: Double = 1.0, name: String? = null) : Distribution, ContinuousDistributionIfc, GetRVariableIfc, RVParametersTypeIfc

Represents the Triangular distribution with parameters - minimum value, maximum value and most likely value

Parameters

theMin

The minimum value of the distribution

theMode

The mode of the distribution

theMax

The maximum value of the distribution

name

an optional label/name

Constructors

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constructor(parameters: DoubleArray)

Constructs a Triangular distribution with min = parameters0, mode = parameters1, max = parameters2

constructor(theMin: Double = 0.0, theMode: Double = 0.0, theMax: Double = 1.0, name: String? = null)

Types

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object Companion

Properties

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open override val id: Int
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Gets the kurtosis of the distribution mu4/mu2^2, www.mathworld.wolfram.com/Kurtosis.html www.mathworld.wolfram.com/TriangularDistribution.html

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open override var label: String?
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myMax the maximum value of the distribution

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myMin the minimum value of the distribution

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myMax the maximum value of the distribution

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open override val name: String
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myRange = myMax - myMin

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open override val rvParameters: RVParameters

the parameters for this type of random variable

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Gets the skewness of the distribution mu3/mu2^(3/2), www.mathworld.wolfram.com/Skewness.html www.mathworld.wolfram.com/TriangularDistribution.html

Functions

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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

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

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open override fun domain(): Interval
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open override fun instance(): Triangular
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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

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open fun likelihood(data: DoubleArray): Double

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.

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open override fun logLikelihood(x: Double): Double

Computes the natural log of the pdf function evaluated at x. Implementations may want to specify computationally efficient formulas for this function.

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open override fun mean(): Double

Returns the mean or expected value of a distribution

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open override fun parameters(): DoubleArray

Gets the parameters for the distribution params0 min The minimum value of the distribution params1 mode The mode of the distribution params2 max The maximum value of the distribution

open override fun parameters(params: DoubleArray)

Sets the parameters for the distribution params0 min The minimum value of the distribution params1 mode The mode of the distribution params2 max The maximum value of the distribution

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open override fun pdf(x: Double): Double

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

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open override fun randomVariable(stream: RNStreamIfc): RVariableIfc
open fun randomVariable(streamNum: Int): RVariableIfc
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fun setParameters(min: Double, mode: Double, max: Double)

Sets the minimum, most likely and maximum value of the triangular distribution to the private data members myMin, myMode and myMax resp throws IllegalArgumentException when the min >mode, min >= max, mode > max

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

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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.

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open override fun toString(): String
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open override fun variance(): Double

Returns the variance of the distribution if defined