Interface RngDistributionsInterface

A version of RngInterface that includes lots of extra distributions.

Depending on your integration, you may not need this.

interface RngDistributionsInterface {
    bates(options?: {
        n?: number;
    }): number;
    bates(n?: number): number;
    batesgaussian(n: number): number;
    batesgaussian(options?: {
        n?: number;
    }): number;
    bernoulli(options?: {
        p?: number;
    }): number;
    bernoulli(p?: number): number;
    beta(options?: {
        alpha?: number;
        beta?: number;
    }): number;
    betaBinomial(options?: {
        alpha?: number;
        beta?: number;
        n?: number;
    }): number;
    binomial(options?: {
        n?: number;
        p?: number;
    }): number;
    cauchy(options?: {
        median?: number;
        scale?: number;
    }): number;
    chiSquared(options?: {
        k?: number;
    }): number;
    chiSquared(k?: number): number;
    exponential(options?: {
        rate?: number;
    }): number;
    exponential(rate?: number): number;
    gamma(options?: {
        rate?: number;
        scale?: number;
        shape?: number;
    }): number;
    hermite(options?: {
        lambda1?: number;
        lambda2?: number;
    }): number;
    hypergeometric(options?: {
        k?: number;
        K?: number;
        n?: number;
        N?: number;
    }): number;
    irwinHall(options?: {
        n?: number;
    }): number;
    irwinHall(n?: number): number;
    kumaraswamy(options?: {
        alpha?: number;
        beta?: number;
    }): number;
    laplace(options?: {
        mean?: number;
        scale?: number;
    }): number;
    logistic(options?: {
        mean?: number;
        scale?: number;
    }): number;
    logNormal(options?: {
        mean?: number;
        stddev?: number;
    }): number;
    pareto(options?: {
        location?: number;
        scale?: number;
        shape?: number;
    }): number;
    poisson(options?: {
        lambda?: number;
    }): number;
    poisson(lambda?: number): number;
    rademacher(): -1 | 1;
    rayleigh(options?: {
        scale?: number;
    }): number;
    rayleigh(scale?: number): number;
    studentsT(options?: {
        nu?: number;
    }): number;
    studentsT(nu?: number): number;
    wignerSemicircle(options?: {
        R?: number;
    }): number;
    wignerSemicircle(R?: number): number;
}

Implemented by

Distributions

bates batesgaussian bernoulli beta betaBinomial binomial cauchy chiSquared exponential gamma hermite hypergeometric irwinHall kumaraswamy laplace logistic logNormal pareto poisson rademacher rayleigh studentsT wignerSemicircle

Distributions

bates

  • bates(options?): number

  • Mean of n uniformly distributed values

    Support: [0, 1]

    Parameters

    • Optionaloptions: {
          n?: number;
      }
      • Optionaln?: number

        Number of values to sum

    Returns number

    The mean of n uniform values

    Example

    rng.bates({ n: 6 });
    rng.bates(6);

    See

    Bates Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

  • bates(n?): number

  • Mean of n uniformly distributed values

    Support: [0, 1]

    Parameters

    • Optionaln: number

      Number of values to sum

    Returns number

    The mean of n uniform values

    Example

    rng.bates({ n: 6 });
    rng.bates(6);

    See

    Bates Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

batesgaussian

  • batesgaussian(n): number

  • A version of the bates distribution that returns gaussian normally distributed results, with n acting as a shape parameter.

    Parameters

    • n: number

      Number of values to sum

    Returns number

    The mean of n uniform values

    See

    Bates Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

  • batesgaussian(options?): number

  • A version of the bates distribution that returns gaussian normally distributed results, with n acting as a shape parameter.

    Parameters

    • Optionaloptions: {
          n?: number;
      }
      • Optionaln?: number

        Number of values to sum

    Returns number

    The mean of n uniform values

    See

    Bates Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

bernoulli

  • bernoulli(options?): number

  • Probability that random number is less than p, returns 1 or 0.

    Support: {0, 1}

    Parameters

    • Optionaloptions: {
          p?: number;
      }
      • Optionalp?: number

        The probability of success, from [0 to 1], default 0.5

    Returns number

    1 or 0, depending on if random number was less than p

    Example

    rng.bernoulli({ p: 0.5 });
    rng.bernoulli(0.5);

    See

    Bernoulli distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

  • bernoulli(p?): number

  • Probability that random number is less than p, returns 1 or 0.

    Support: {0, 1}

    Parameters

    • Optionalp: number

      The probability of success, from [0 to 1], default 0.5

    Returns number

    1 or 0, depending on if random number was less than p

    Example

    rng.bernoulli({ p: 0.5 });
    rng.bernoulli(0.5);

    See

    Bernoulli distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

beta

  • beta(options?): number

  • Generates a value from the Beta distribution.

    Support: (0, 1)

    Parameters

    • Optionaloptions: {
          alpha?: number;
          beta?: number;
      }
      • Optionalalpha?: number

        The alpha parameter of the Beta distribution, must be positive, default 0.5.

      • Optionalbeta?: number

        The beta parameter of the Beta distribution, must be positive, default 0.5.

    Returns number

    A value from the Beta distribution, (0, 1).

    Example

    rng.beta({ alpha = 0.5, beta = 0.5 })
    rng.beta({ alpha = 1, beta = 2 })
    rng.beta({ beta = 1 })

    See

    Beta distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

betaBinomial

  • betaBinomial(options?): number

  • Generates a value from the Beta-binomial distribution.

    Support: {0, 1, 2, ..., n}

    Parameters

    • Optionaloptions: {
          alpha?: number;
          beta?: number;
          n?: number;
      }
      • Optionalalpha?: number

        The alpha parameter of the Beta distribution, default 1, must be positive.

      • Optionalbeta?: number

        The beta parameter of the Beta distribution, default 1, must be positive.

      • Optionaln?: number

        The number of trials, default 1, must be positive integer.

    Returns number

    The number of successes in n trials, {0, 1, 2, ..., n}

    Example

    rng.betaBinomial({ alpha = 1, beta = 2, n = 10 })
    rng.betaBinomial({ n = 100 })

    See

    Beta-binomial distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

binomial

  • binomial(options?): number

  • Generates a value from the Binomial distribution.

    Probability distribution of getting number of successes of n trials of a boolean trial with probability p

    Support: {0, 1, 2, ..., n}

    Parameters

    • Optionaloptions: {
          n?: number;
          p?: number;
      }
      • Optionaln?: number

        The number of trials, must be positive integer, default 1.

      • Optionalp?: number

        The probability of success, must be a number between 0 and 1 inclusive, default 0.5.

    Returns number

    The number of successes, {0, 1, 2, ..., n}.

    Example

    rng.binomial({ n = 1, p = 0.5 });
    rng.binomial({ n = 100, p = 0.1 });

    See

    Binomial distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

cauchy

  • cauchy(options?): number

  • Generates a value from the Cauchy distribution.

    Support: (-∞, +∞)

    @example:

    rng.cauchy({ median: 2, scale: 1 }) rng.cauchy({ median: 2 }) rng.cauchy({ scale: 1 })

    Parameters

    • Optionaloptions: {
          median?: number;
          scale?: number;
      }
      • Optionalmedian?: number

        The location parameter (median, sometimes called x0) - default 0.

      • Optionalscale?: number

        The scale parameter, must be positive - default 1.

    Returns number

    A value from the Cauchy distribution (-∞, +∞).

    See

    Cauchy Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

chiSquared

  • chiSquared(options?): number

  • Generates a value from the Chi-squared distribution.

    Support: [0, ∞)

    @example:

    rng.chiSquared({ k: 2 }) rng.chiSquared(2) // Equivalent

    Parameters

    • Optionaloptions: {
          k?: number;
      }
      • Optionalk?: number

        The degrees of freedom, must be a postive integer - default 1.

    Returns number

    A value from the Chi-squared distribution [0, ∞).

    See

    Chi-squared Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameter is not valid.

  • chiSquared(k?): number

  • Generates a value from the Chi-squared distribution.

    Support: [0, ∞)

    @example:

    rng.chiSquared({ k: 2 }) rng.chiSquared(2) // Equivalent

    Parameters

    • Optionalk: number

      The degrees of freedom, must be a postive integer - default 1..

    Returns number

    A value from the Chi-squared distribution [0, ∞).

    See

    Chi-squared Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameter is not valid.

exponential

  • exponential(options?): number

  • This function uses the inverse transform sampling method to generate an exponentially distributed random variable.

    Support: [0, ∞)

    Parameters

    • Optionaloptions: {
          rate?: number;
      }
      • Optionalrate?: number

        The rate, must be > 0, default 1

    Returns number

    Example

    rng.exponential({ rate: 1 });
    rng.exponential(1);

    See

    Exponential distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

  • exponential(rate?): number

  • This function uses the inverse transform sampling method to generate an exponentially distributed random variable.

    Support: [0, ∞)

    Parameters

    • Optionalrate: number

      The rate, must be > 0, default 1

    Returns number

    Example

    rng.exponential({ rate: 1 });
    rng.exponential(1);

    See

    Exponential distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

gamma

  • gamma(options?): number

  • Generates a random number from the Gamma distribution.

    Support: (0, ∞)

    Parameters

    • Optionaloptions: {
          rate?: number;
          scale?: number;
          shape?: number;
      }
      • Optionalrate?: number

        The rate parameter, must be postive, default 1.

      • Optionalscale?: number

        The scale parameter, must be postive, ( = 1/rate).

      • Optionalshape?: number

        The shape parameter, must be postive, default 1.

    Returns number

    A random number from the Gamma distribution, from (0, ∞).

    Example

    rng.gamma({ shape = 0.5, rate = 0.5 })
    rng.gamma({ shape = 0.5, scale = 2 })
    rng.gamma({ shape = 0.5, rate = 0.5, scale = 2 }) // Redundant as scale = 1 / rate
    rng.gamma({ shape = 0.5, rate = 2, scale = 2 }) // Error('Cannot supply scale and rate')

    See

    Throws

    If both scale and rate are given and are not reciprocals of each other

    Throws

    NumberValidationError If the input parameters are not valid.

hermite

  • hermite(options?): number

  • Generates a value from the Hermite distribution.

    Support: {0, 1, 2, 3, ...}

    @example:

    rng.hermite({ lambda1: 1, lambda2: 2 }) rng.hermite({ lambda1: 1 }) rng.hermite({ lambda2: 2 })

    Parameters

    • Optionaloptions: {
          lambda1?: number;
          lambda2?: number;
      }
      • Optionallambda1?: number

        The mean of the first Poisson process, must be positive.

      • Optionallambda2?: number

        The mean of the second Poisson process, must be positive.

    Returns number

    A value from the Hermite distribution, {0, 1, 2, 3, ...}

    See

    Hermite Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

hypergeometric

  • hypergeometric(options?): number

  • This function uses combinations to calculate probabilities for the hypergeometric distribution.

    The hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature

    Support: {max(0, n+K-N), ..., min(n, K)}

    Parameters

    • Optionaloptions: {
          k?: number;
          K?: number;
          n?: number;
          N?: number;
      }
      • Optionalk?: number

        The number of observed successes, must be positive integer lteq K and n.

      • OptionalK?: number

        The number of successes in the population, must be positive integer lteq N.

      • Optionaln?: number

        The number of draws, must be positive integer lteq N.

      • OptionalN?: number

        The population size, must be positive integer.

    Returns number

    The probability of exactly k successes in n draws, {max(0, n+K-N), ..., min(n, K)}.

    Example

    rng.hypergeometric({ N: 50, K: 10, n: 5 });
    rng.hypergeometric({ N: 50, K: 10, n: 5, k: 2 });

    See

    Hypergeometric distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

irwinHall

kumaraswamy

  • kumaraswamy(options?): number

  • Generates a value from the Kumaraswamy distribution.

    Support: (0, 1)

    @example:

    rng.kumaraswamy({ alpha: 1, beta: 2 }) rng.kumaraswamy({ alpha: 1 }) rng.kumaraswamy({ beta: 2 })

    Parameters

    • Optionaloptions: {
          alpha?: number;
          beta?: number;
      }
      • Optionalalpha?: number

        The first shape parameter of the Kumaraswamy distribution, must be positive.

      • Optionalbeta?: number

        The second shape parameter of the Kumaraswamy distribution, must be positive.

    Returns number

    A value from the Kumaraswamy distribution, (0, 1).

    See

    Kumaraswamy Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

laplace

  • laplace(options?): number

  • Generates a value from the Laplace distribution.

    Support: (-∞, +∞)

    @example:

    rng.laplace({ mean: 2, scale: 1 }) rng.laplace({ mean: 2 }) rng.laplace({ scale: 1 })

    Parameters

    • Optionaloptions: {
          mean?: number;
          scale?: number;
      }
      • Optionalmean?: number

        The location parameter (mean) - default 0.

      • Optionalscale?: number

        The scale parameter, must be positive - default 1.

    Returns number

    A value from the Laplace distribution (-∞, +∞).

    See

    Laplace Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

logistic

  • logistic(options?): number

  • Generates a value from the Logistic distribution.

    Support: (-∞, +∞)

    @example:

    rng.logistic({ mean: 2, scale: 1 }) rng.logistic({ mean: 2 }) rng.logistic({ scale: 1 })

    Parameters

    • Optionaloptions: {
          mean?: number;
          scale?: number;
      }
      • Optionalmean?: number

        The location parameter (mean) - default 0.

      • Optionalscale?: number

        The scale parameter, must be positive - default 1.

    Returns number

    A value from the Logistic distribution (-∞, +∞).

    See

    Laplace Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

logNormal

  • logNormal(options?): number

  • Generates a value from the Log-Normal distribution.

    Support: (0, ∞)

    @example:

    rng.logNormal({ mean: 2, stddev: 1 }) rng.logNormal({ mean: 2 }) rng.logNormal({ stddev: 1 })

    Parameters

    • Optionaloptions: {
          mean?: number;
          stddev?: number;
      }
      • Optionalmean?: number

        The mean of the underlying normal distribution - default 0.

      • Optionalstddev?: number

        The standard deviation of the underlying normal distribution, must be positive - default 1.

    Returns number

    A value from the Log-Normal distribution (0, ∞).

    See

    Log Normal Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

pareto

  • pareto(options?): number

  • Generates a value from the Generalized Pareto distribution.

    Support: [scale, ∞)

    Parameters

    • Optionaloptions: {
          location?: number;
          scale?: number;
          shape?: number;
      }
      • Optionallocation?: number

        The location parameter, default 0.

      • Optionalscale?: number

        The scale parameter, must be positive ( > 0), default 1.

      • Optionalshape?: number

        The shape parameter, must be >= 0, default 0.5.

    Returns number

    A value from the Generalized Pareto distribution, [scale, ∞).

    Example

    rng.pareto({ shape: 0.5, scale: 1, location: 0 });
    rng.pareto({ location: 0 });
    rng.pareto({ scale: 1 });
    rng.pareto({ shape: 0.5 });

    See

    Pareto distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

poisson

  • poisson(options?): number

  • This function uses the fact that the Poisson distribution can be generated using a series of random numbers multiplied together until their product is less than e^(-lambda). The number of terms needed is the Poisson-distributed random variable.

    Support: {1, 2, 3 ...}

    Parameters

    • Optionaloptions: {
          lambda?: number;
      }
      • Optionallambda?: number

        Control parameter, must be positive, default 1.

    Returns number

    Poisson distributed random number, {1, 2, 3 ...}

    Example

    rng.poisson({ lambda: 1 });
    rng.poisson(1);

    See

    Poisson distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

  • poisson(lambda?): number

  • This function uses the fact that the Poisson distribution can be generated using a series of random numbers multiplied together until their product is less than e^(-lambda). The number of terms needed is the Poisson-distributed random variable.

    Support: {1, 2, 3 ...}

    Parameters

    • Optionallambda: number

      Control parameter, must be positive, default 1.

    Returns number

    Poisson distributed random number, {1, 2, 3 ...}

    Example

    rng.poisson({ lambda: 1 });
    rng.poisson(1);

    See

    Poisson distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

rademacher

  • rademacher(): -1 | 1

  • Generates a value from the Rademacher distribution.

    Support: {-1, 1}

    Returns -1 | 1

    either -1 or 1 with 50% probability

    Example

    rng.rademacher();

    See

    Rademacher distribution

rayleigh

  • rayleigh(options?): number

  • Generates a value from the Rayleigh distribution

    Support: [0, ∞)

    @example:

    rng.rayleigh({ scale: 2 }) rng.rayleigh(2) // Equivalent

    Parameters

    • Optionaloptions: {
          scale?: number;
      }
      • Optionalscale?: number

        The scale parameter of the Rayleigh distribution, must be > 0 - default 1.

    Returns number

    A value from the Rayleigh distribution [0, ∞).

    See

    Rayleigh Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameter is not valid.

  • rayleigh(scale?): number

  • Generates a value from the Rayleigh distribution

    Support: [0, ∞)

    @example:

    rng.rayleigh({ scale: 2 }) rng.rayleigh(2) // Equivalent

    Parameters

    • Optionalscale: number

      The scale parameter of the Rayleigh distribution, must be > 0 - default 1.

    Returns number

    A value from the Rayleigh distribution [0, ∞).

    See

    Rayleigh Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameter is not valid.

studentsT

  • studentsT(options?): number

  • Generates a value from the Student's t-distribution.

    Support: (-∞, ∞)

    @example:

    rng.studentsT({ nu: 10 }) rng.studentsT(10)

    Parameters

    • Optionaloptions: {
          nu?: number;
      }
      • Optionalnu?: number

        The degrees of freedom, default 1, must be positive.

    Returns number

    A value from the Student's t-distribution, (-∞, ∞).

    See

    Student's t-distribution - Wikipedia

    Throws

    NumberValidationError If the input parameter is not valid.

  • studentsT(nu?): number

  • Generates a value from the Student's t-distribution.

    Support: (-∞, ∞)

    @example:

    rng.studentsT({ nu: 10 }) rng.studentsT(10)

    Parameters

    • Optionalnu: number

      The degrees of freedom, must be positive, default 1

    Returns number

    A value from the Student's t-distribution, (-∞, ∞).

    See

    Student's t-distribution - Wikipedia

    Throws

    NumberValidationError If the input parameter is not valid.

wignerSemicircle

  • wignerSemicircle(options?): number

  • Generates a value from the Wigner semicircle distribution.

    Support: [-R; +R]

    @example:

    rng.wignerSemicircle({ R: 1 }) rng.wignerSemicircle(1)

    Parameters

    • Optionaloptions: {
          R?: number;
      }
      • OptionalR?: number

        The radius of the semicircle, must be positive, default 1.

    Returns number

    A value from the Wigner semicircle distribution, [-R; +R].

    See

    Wigner Semicircle Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

  • wignerSemicircle(R?): number

  • Generates a value from the Wigner semicircle distribution.

    Support: [-R; +R]

    @example:

    rng.wignerSemicircle({ R: 1 }) rng.wignerSemicircle(1)

    Parameters

    • OptionalR: number

      The radius of the semicircle, must be positive, default 1.

    Returns number

    A value from the Wigner semicircle distribution, [-R; +R].

    See

    Wigner Semicircle Distribution - Wikipedia

    Throws

    NumberValidationError If the input parameters are not valid.

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