tpdf — Evaluate the Student's t probability density function.
tpdf(x,nu) evaluates the probability density of the Student's t distribution with nu degrees of freedom at x.
Syntax
y = tpdf(x, nu)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
x | Any | Yes | — | Evaluation point. |
nu | Any | Yes | — | Degrees of freedom parameter. |
Returns
| Name | Type | Description |
|---|---|---|
y | NumericArray | Distribution function value. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:tpdf:InvalidArgument | Inputs are nonnumeric, sizes are incompatible, or too many arguments are supplied. | normal distribution: invalid argument |
RunMat:tpdf:Internal | Internal tensor conversion or allocation fails. | normal distribution: internal error |
How tpdf works
- Documented
xandnuinputs are single or double scalars and arrays. Inputs may have the same size, or either input may be scalar. - The result is single when either documented floating input is single; otherwise it is double.
- RunMat mode additionally accepts logical and all eight native integer classes. Integer values must be exactly representable at the binary64 PDF boundary.
- Scalar inputs broadcast over matching-size array inputs.
- Nonpositive or
NaNdegrees of freedom produceNaNelementwise. nu = Infuses the standard normal density.
GPU memory and residency
Resident inputs preserve their floating precision and return through the provider that owns the input. When no direct provider PDF kernel is available, the values gather once for host evaluation and the result is restored to that owner.
Example
Cauchy density at zero
y = tpdf(0, 1)Using tpdf with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how tpdf changes the result.
Run a small tpdf example, explain the result, then change one input and compare the output.
FAQ
What is nu?⌄
nu is the degrees-of-freedom parameter for the Student's t distribution.
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 · normcdf · norminv · normpdf · onehotdecode · onehotencode · pdf · prctile · quantile · refline · rmse · skewness · tabulate · tcdf · tiedrank · tinv · 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 tpdf is executed, line by line, in Rust.
- View the source for tpdf 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.