# Continuous CDF VI

LabVIEW 2011 Help

Edition Date: June 2011

Part Number: 371361H-01

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Owning Palette: Probability VIs

Requires: Full Development System

Computes the continuous cumulative distribution function (CDF), or the probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. You must manually select the polymorphic instance to use.

Use the pull-down menu to select an instance of this VI.

 Select an instance Beta CDFCauchy CDFChi-Squared CDFChi-Squared (Non-Central) CDFExp CDFExtreme Value CDFF CDFGamma CDFLaplace CDFLogistic CDFLognormal CDFNormal CDFPareto CDFRayleigh CDFStudent t CDFTriangular CDFUniform CDFWeibull CDF

## Beta CDF

 x specifies the quantile of the continuous random variate and is bounded by the interval [0, 1]. a specifies the first shape parameter of the beta variate. b specifies the second shape parameter of the beta variate. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Cauchy CDF

 Note  X represents a Cauchy-distributed variate with location parameter a and scale parameter b, and whose mean and variance are undefined. This function also is known as the Cauchy cumulative distribution function (CDF) or the Cauchy distribution function.

 x specifies the quantile of the continuous random variate. a specifies the location parameter and median of the variate. b specifies the scale parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Chi-Squared CDF

 Note  X represents a chi-squared-distributed variate with k degrees of freedom. The sum of k squared, independent, standard normal variates is distributed as a chi-squared variate with k degrees of freedom. This function also is known as the chi-squared cumulative distribution function (CDF) or the chi-squared distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ 0. k specifies the number of degrees of freedom and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Chi-Squared (Non-Central) CDF

 Note  X represents a non-central chi-squared-distributed variate with k degrees of freedom and a noncentrality parameter d. The sum of k squared, independent, normal variates with a mean of d and a standard deviation of 1 is distributed as a non-central chi-squared variate with k degrees of freedom and noncentrality d. This function also is known as the non-central chi-squared cumulative distribution function (CDF), the non-central chi-squared distribution function, or the generalized Rayleigh, Rayleigh-Rice, or Ricean distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ 0. k specifies the number of degrees of freedom and must be greater than 0. d specifies the noncentrality parameter, which must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Exp CDF

 Note  X represents an exponential-distributed variate. The exponential distribution often is used to model Poisson processes, which are situations in which an object can change from one state to another with constant probability per unit time. The scale parameter b is the mean of the distribution. This function also is known as the exponential cumulative distribution function (CDF) or the exponential distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ a. a specifies the offset parameter of the variate. b specifies the scale parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Extreme Value CDF

 Note  X represents an extreme value variate, which is the distribution of the largest extreme of a number of values with location parameter a and scale parameter b. This function also is known as the extreme value cumulative distribution function (CDF), the extreme value distribution function, or the Gumbel distribution.

 x specifies the quantile of the continuous random variate. a specifies the location parameter of the variate. b specifies the scale parameter of the variate. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## F CDF

 Note  X represents an F variate, which is the ratio of two chi-squared variates. The F variate provides a basis for comparing variances between data and factors within a model, often indicating which factors cause significant variation. The k1 and k2 parameters specify the degrees of freedom of the two chi-squared variates whose ratio form the F variate. This function also is known as the F cumulative distribution function (CDF) or the F distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ 0. k1 specifies the number of degrees of freedom of the first chi-squared variate that forms the F variate. k1 must be greater than 0. k2 specifies the number of degrees of freedom of the second chi-squared variate that forms the F variate. k2 must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Gamma CDF

 Note  X represents a gamma-distributed variate with scale parameter b and shape parameter c. The gamma distribution includes the chi-squared, Erlang, and exponential distributions as special cases, but the value of the gamma shape parameter is not restricted to integers. The gamma variate with an integer shape parameter c is known as the Erlang variate. This function also is known as the gamma cumulative distribution function (CDF) or the gamma distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ 0. b specifies the scale parameter of the variate and must be greater than 0. c specifies the shape parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Laplace CDF

 Note  X represents a Laplace-distributed variate with location parameter a and scale parameter b. This function also is known as the Laplace cumulative distribution function (CDF), the Laplace distribution function, or the double-exponential distribution.

 x specifies the quantile of the continuous random variate. a specifies the location or mean parameter of the variate. b specifies the scale parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Logistic CDF

 Note  X represents a logistic-distributed variate with location parameter a and scale parameter b. You can use the logistic variate to model growth. This function also is known as the logistic cumulative distribution function (CDF) or the logistic distribution function.

 x specifies the quantile of the continuous random variate. a specifies the location or mean parameter of the variate. b specifies the scale parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Lognormal CDF

 Note  X represents a lognormal-distributed variate, which always is nonnegative and has several large values. This function also is known as the lognormal cumulative distribution function (CDF) or the lognormal distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ 0. b specifies the scale or median parameter of the variate and must be greater than 0. c specifies the shape parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Normal CDF

 Note  X represents a normally-distributed variate with location parameter mean and scale parameter std. The normal continuous distribution is the most commonly used distribution in statistics and is the asymptotic form of the sum of random variables under a wide range of conditions. This function also is known as the normal cumulative distribution function (CDF), the normal distribution function, or the Gaussian distribution.

 x specifies the quantile of the continuous random variate. mean specifies the location or mean parameter of the variate. std specifies the scale or standard deviation parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Pareto CDF

 Note  X represents a Pareto-distributed variate with location parameter a and shape parameter c. You can use the Pareto distribution to model the distribution of the number of people with an income less than x. The Pareto distribution often is associated with the "80/20" rule. This function also is known as the Pareto cumulative distribution function (CDF) or the Pareto distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ a. a specifies the location parameter and must be greater than 0. c specifies the shape parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Rayleigh CDF

 Note  X represents a Rayleigh-distributed variate with scale parameter b. The RMS sum of two independent, standard, normal variates is a Rayleigh-distributed variate. This function also is known as the Rayleigh cumulative distribution function (CDF) or the Rayleigh distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ 0. b specifies the scale parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Student t CDF

 Note  X represents a Student's t-distributed variate with k degrees of freedom. You can use the Student's t-distribution to test whether two samples came from the same normal population or whether the differences between the means of two samples is statistically significant. This function also is known as the Student's t cumulative distribution function (CDF) or the Student's t-distribution function.

 x specifies the quantile of the continuous random variate. k degrees of freedom specifies the number of degrees of freedom and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. 1–cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value greater than x. error returns any error or warning condition from the VI.

## Triangular CDF

 Note  X represents a triangular-distributed variate with lower limit xmin, upper limit xmax, and mode xmode. This function also is known as the triangular cumulative distribution function (CDF) or the triangular distribution function.

 x specifies the quantile of the continuous random variate and is bounded by the interval [xmin, xmax]. xmin specifies the lower limit parameter of the variate. xmode specifies the mode parameter of the variate. The default is NaN, which corresponds to a mode at the midpoint between xmin and xmax. xmax specifies the upper limit parameter of the variate. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Uniform CDF

 Note  X represents a continuous uniform-distributed variate such that every value in the range of x, as defined by the interval [xmin, xmax], is equally likely to occur. Uniform random numbers typically follow this distribution. The continuous uniform distribution serves as the basis of the generation of random numbers from other statistical distributions. This function also is known as the uniform cumulative distribution function (CDF), the uniform distribution function, or the rectangular distribution.

 x specifies the quantile of the continuous random variate and is bounded by the interval [xmin, xmax]. xmin specifies the lower limit parameter of the variate. xmax specifies the upper limit parameter of the variate. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Weibull CDF

 Note  X represents a Weibull-distributed variate with scale parameter a and shape parameter b. You can use the Weibull distribution as a lifetime distribution to study reliability. This function also is known as the Weibull cumulative distribution function (CDF) or the Weibull distribution function.

 x specifies the quantile of the continuous random variate with range x ≥ 0. a specifies the location parameter and must be greater than 0. b specifies the shape parameter of the variate and must be greater than 0. cdf(x) returns the cumulative probability that the random variate X, where X describes the selected distribution type, has a value less than or equal to x. error returns any error or warning condition from the VI.

## Continuous CDF Details

When you use the Beta CDF instance of this VI, X represents a beta-distributed variate, which is restricted to a finite interval [0, 1], with given shape parameters a and b.

The CDF function with a beta distribution also is known as the beta cumulative distribution function (CDF), the beta distribution function, or the incomplete beta function.

## Example

Refer to the Display Continuous Probability Distributions VI in the labview\examples\analysis\statxmpl.llb for an example of using the Continuous CDF VI.

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