Continuous Inverse CDF VI

Beta Inverse CDF

	cdf(x) is the cumulative probability Prob[X ≤ x].
	a specifies the first shape parameter of the beta variate.
	b specifies the second shape parameter of the beta variate.
	x specifies the quantile of the continuous random variate and is bounded by the interval [0, 1].
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Cauchy Inverse CDF

X represents a Cauchy-distributed variate with location parameter a, scale parameter b, and whose moments (mean and variance) are undefined.

This function is also known as the Cauchy inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	a specifies the location parameter and median of the variate.
	b specifies the scale parameter of the variate and must be greater than 0.
	x is the quantile of the continuous random variate.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Chi-Squared (Non-Central) Inverse CDF

X represents a non-central chi-squared-distributed variate with k degrees of freedom and noncentrality parameter d. The sum of k squared independent normal variates (with mean = d and standard deviation 1) is distributed as a non-central chi-squared variate with k degrees of freedom and noncentrality d.

This function is also known as the non-central chi-squared inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	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.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Chi-Squared Inverse CDF

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 is also known as the chi-squared inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	k specifies the number of degrees of freedom and must be greater than 0.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Exp Inverse CDF

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 also the mean of the distribution.

This function is also known as the exponential inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	a specifies the offset parameter of the variate.
	b specifies the scale parameter of the variate and must be greater than 0.
	x is the quantile of the continuous random variate with range x is greater than or equal to a.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Extreme Value Inverse CDF

X represents an extreme value variate: the distribution of the largest extreme of a number of values with location parameter a and scale parameter b.

This function is also known as the extreme value inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	a specifies the location parameter and median of the variate.
	b specifies the scale parameter of the variate.
	x is the quantile of the continuous random variate.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

F Inverse CDF

X represents an F variate which is defined as the ratio of two chi-squared variates; it provides a basis for comparing variances between data and factors within a model, often indicating which factors cause significant variation. Two parameters, k1 and k2, define the degrees of freedom of the two chi-squared variates whose ratio form the F variate.

This function is also known as the F inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	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.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Gamma Inverse CDF

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 gamma shape parameter is not restricted to be an integer. The gamma variate with an integer shape parameter c is known as the Erlang variate.

This function is also known as the gamma inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	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.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Laplace Inverse CDF

X represents a Laplace-distributed variate with location parameter a and scale parameter b.

This function is also known as the Laplace inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	a specifies the location or mean parameter of the variate.
	b specifies the scale or median parameter of the variate and must be greater than 0.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Logistic Inverse CDF

X represents a logistic-distributed variate with location parameter a and scale parameter b. The logistic variate is often used to model growth.

This function is also known as the logistic inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	a specifies the location or mean parameter of the variate.
	b specifies the scale or median parameter of the variate and must be greater than 0.
	x is the quantile of the continuous random variate.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Lognormal Inverse CDF

X represents a lognormal-distributed variate, which is always nonnegative and has a few very large values.

This function is also known as the lognormal inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	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.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Normal Inverse CDF

X represents a normally-distributed variate with location parameter mean and scale parameter std. It 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 is also known as the normal inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	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.
	x is the quantile of the continuous random variate.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Pareto Inverse CDF

X represents a Pareto-distributed variate with location parameter a and shape parameter c. The Pareto distribution can be used to model the distribution of income (the number of people with an income less than x) and is often associated with the "80/20" rule.

This function is also known as the Pareto inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	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.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Rayleigh Inverse CDF

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 is also known as the Rayleigh inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	b specifies the scale or median parameter of the variate and must be greater than 0.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Student t Inverse CDF

X represents a Student's t distributed variate with k degrees of freedom. The Student's t distribution is often used to test whether two samples were drawn from the same normal population or whether the differences between the means of two samples is statistically significant.

This function is also known as the Student's t inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	k degrees of freedom specifies the number of degrees of freedom and must be greater than 0.
	x specifies the quantile of the continuous random variate.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Triangular Inverse CDF

X represents a triangular-distributed variate with lower limit xmin, upper limit xmax, and mode xmode.

This function is also known as the triangular inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	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.
	x is the quantile of the continuous random variate and within the interval [xmin, xmax].
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Uniform Inverse CDF

X represents a continuous uniform distributed variate where every value in the range of x, as defined by the interval [xmin, xmax], is equally likely to occur. This is typically the distribution taken by uniform random numbers and serves as the basis of the generation of random numbers from other statistical distributions.

This function is also known as the uniform inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	xmin specifies the lower limit parameter of the variate.
	xmax specifies the upper limit parameter of the variate.
	x is the quantile of the continuous random variate and within the interval [xmin, xmax].
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Weibull Inverse CDF

X represents a Weibull-distributed variate with scale parameter a and shape parameter b. The Weibull distribution is often used as a lifetime distribution to study reliability.

This function is also known as the Weibull inverse cumulative distribution function (inverse CDF).

	cdf(x) is the cumulative probability Prob[X ≤ x].
	a specifies the scale parameter of the variate and must be greater than 0.
	b specifies the shape parameter of the variate and must be greater than 0.
	x is the quantile of the continuous random variate with range x is greater than or equal to 0.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Continuous Inverse CDF Details

The Beta Inverse CDF instance finds the value x such that cdf(x) is the probability that the random variate X, where X describes the selected distribution type, takes on a value less than or equal to it.

Prob[X ≤ x] = cdf(x)

Example

Refer to the Display Continuous Probability Distributions VI in the labview\examples\Mathematics\Probability and Statistics directory for an example of using the Continuous Inverse CDF VI.

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