normcdf — Evaluate the normal cumulative distribution function.
normcdf(x) evaluates the standard normal CDF. normcdf(x,mu) and normcdf(x,mu,sigma) evaluate a normal distribution with mean mu and standard deviation sigma. normcdf(...,"upper") returns the upper-tail probability.
Syntax
p = normcdf(x)
p = normcdf(x, mu)
p = normcdf(x, mu, sigma)
p = normcdf(x, mu, sigma, "upper")Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
x | Any | Yes | — | Evaluation point. |
mu | Any | No | 0 | Mean parameter. |
sigma | Any | No | 1 | Standard deviation parameter. |
Returns
| Name | Type | Description |
|---|---|---|
y | NumericArray | Distribution function value. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:normcdf:InvalidArgument | Inputs are nonnumeric, sizes are incompatible, or too many arguments are supplied. | normal distribution: invalid argument |
RunMat:normcdf:Internal | Internal tensor conversion or allocation fails. | normal distribution: internal error |
How normcdf works
x,mu, andsigmamay be scalars or matching-size numeric arrays.- MATLAB-compatible numeric inputs are single or double. Typed integers and logical values in any numeric role are independently gated RunMat extensions.
- Admitted integer values must be exactly representable as double. Any single floating input selects single output; otherwise output is double.
- Negative
sigmavalues produceNaNelementwise. sigma = 0returns a step atmu."upper"uses the complementary error-function path for better extreme-tail stability.
Examples
Standard normal midpoint
p = normcdf(0)Upper tail
p = normcdf(8, 0, 1, "upper")Using normcdf with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how normcdf changes the result.
Run a small normcdf example, explain the result, then change one input and compare the output.
FAQ
Does normcdf support array inputs?⌄
Yes. Scalar parameters broadcast over matching-size numeric arrays.
Related Stats functions
Summary
binocdf · boxplot · cdf · cdfplot · chi2cdf · corr · corrcoef · corrcov · cov · cov2corr · dummyvar · ecdf · filloutliers · fitdist · geomean · grpstats · harmmean · icdf · isoutlier · kstest · kurtosis · lsline · mad · mode · nanmax · normalize · norminv · normpdf · onehotdecode · onehotencode · pdf · prctile · quantile · refline · rmse · skewness · tabulate · tcdf · tiedrank · tinv · tpdf · ttest2 · wblinv
Ml
bayesopt · classify · confusionmat · crossvalind · cvpartition · fitclinear · fitctree · fitlm · kmeans · knnsearch · lasso · lassoglm · linkage · lscov · mnrfit · optimizableVariable · pdist · pdist2 · perfcurve · predict · regress · ridge · squareform · test · training · tsne
Random
binornd · bootstrp · datasample · dividerand · exprnd · gamrnd · lhsdesign · mvnrnd · normrnd · random · randsample · rng · trnd · unidrnd · unifrnd · wblrnd
Hist
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how normcdf is executed, line by line, in Rust.
- View the source for normcdf in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.
- RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
- Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.