icdf — Evaluate inverse cumulative distribution functions by distribution name or fitted distribution object.

icdf(name,p,...) evaluates inverse cumulative distribution functions for supported named distributions. icdf(pd,p) evaluates quantiles for a ProbabilityDistribution object returned by fitdist.

Syntax

x = icdf("Normal", p)
x = icdf("Normal", p, mu, sigma)
x = icdf("t", p, nu)
x = icdf("Weibull", p, a, b)
x = icdf("Chi-square", p, nu)
x = icdf("Binomial", p, n, prob)

x = icdf("Normal", p)
x = icdf("Normal", p, mu, sigma)
x = icdf("t", p, nu)
x = icdf("Weibull", p, a, b)
x = icdf("Chi-square", p, nu)
x = icdf("Binomial", p, n, prob)
x = icdf("Gamma", p, shape, scale)
x = icdf("Exponential", p, mu)
x = icdf("Poisson", p, lambda)
x = icdf("Uniform", p)
x = icdf("Uniform", p, a, b)
x = icdf("Lognormal", p, mu, sigma)
x = icdf("Beta", p, a, b)
x = icdf("F", p, v1, v2)
x = icdf(pd, p)

Inputs

Returns

Errors

How icdf works

• Supported distribution names include "Normal", "t", "Weibull", "Chi-square", "Binomial", "Gamma", "Exponential", "Poisson", "Uniform", "Lognormal", "Beta", and "F".
• Common aliases are accepted after case-insensitive normalization and removal of punctuation or spaces, including "norm", "gaussian", "student t", "wbl", "chi2", "bino", "gam", "exp", "poiss", "unif", "logn", and "fdist".
• icdf("Normal",p) uses mean 0 and standard deviation 1; icdf("Normal",p,mu,sigma) uses supplied normal parameters.
• icdf("t",p,nu) returns Student's t quantiles for degrees of freedom nu.
• icdf("Weibull",p) uses scale 1 and shape 1; icdf("Weibull",p,a,b) uses supplied Weibull scale and shape.
• icdf("Chi-square",p,nu) inverts the chi-square CDF with degrees of freedom nu.
• icdf("Binomial",p,n,prob) returns the smallest integer outcome whose binomial CDF is at least p.
• icdf("Gamma",p,shape,scale), icdf("Exponential",p,mu), icdf("Poisson",p,lambda), icdf("Beta",p,a,b), and icdf("F",p,v1,v2) require the shown distribution parameters.
• icdf("Uniform",p) uses bounds [0,1]; icdf("Uniform",p,a,b) uses supplied lower and upper bounds.
• icdf("Lognormal",p) uses mean 0 and standard deviation 1 for the underlying normal distribution; icdf("Lognormal",p,mu) and icdf("Lognormal",p,mu,sigma) use supplied lognormal parameters.
• icdf(pd,p) supports fitted normal, exponential, lognormal, gamma, Weibull, and Poisson distribution objects returned by fitdist.
• Scalar and compatible array inputs broadcast to a common output shape. Invalid probabilities or distribution parameters produce NaN elements.
• Continuous distributions return endpoint values at p = 0 and Inf where the upper tail is unbounded at p = 1; bounded distributions return their finite endpoints. The Poisson inverse returns Inf at p = 1.

Examples

Normal median with parameters

x = icdf("Normal", 0.5, 10, 2)

Expected output:

x = 10

Discrete binomial quantile

k = icdf("Binomial", 0.75, 10, 0.5)

Expected output:

k = 6

Uniform quantile with bounds

x = icdf("Uniform", 0.25, 10, 20)

Expected output:

x = 12.5

Fitted distribution median

pd = fitdist([1;2;3], "Normal"); x = icdf(pd, 0.5)

Expected output:

x = 2

Using icdf with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how icdf changes the result.

FAQ

Related Stats functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how icdf is executed, line by line, in Rust.

• View the source for icdf in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

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