[Laasya-73]

Summary

This PR adds a new blog post introducing the Mixture TrueMeasure in QMCPy and exploring two approaches to working with mixture distributions:

• Hierarchical mixture sampling: Generating samples by selecting a component according to its probability.
• Probability-weighted component integration: Estimating expectations for individual components and combining them using their mixture probabilities.

The article explains the motivation through a practical manufacturing example and compares both approaches at equal computational cost.

What's Included

• An introduction to mixture distributions and QMCPy's Mixture implementation.
• A comparison using one-dimensional and correlated higher-dimensional Gaussian mixtures.
• Numerical results from randomized quasi-Monte Carlo experiments, including 100 paired mixture instances.
• Four figures illustrating the mixture distribution and numerical comparisons.
• Practical guidance on when each approach is useful.

[Copilot]

🟡 Changes recommended

The analysis notebook must be publicly accessible and linked so readers can reproduce the numerical results.

1 open issue

• Publish the analysis notebook and provide reproducibility details · New

What changed in this PR

Adds a QMCPy website article introducing mixture sampling and comparing it with probability-weighted component integration.

Changes:

• Explains the Mixture API and equal-evaluation-budget experiments.
• Presents numerical comparisons and practical guidance.
• Adds article-specific styling for wide equations.

File	Description
blogs/​mixed-distributions-in-qmcpy/​index.qmd	Introduces mixture distributions, examples, and numerical comparisons.
blogs/​mixed-distributions-in-qmcpy/​equations.css	Enables horizontal scrolling for wide display equations.

_{Review effort: Balanced}