Explore some of the properties of density estimation in the following way. (a) Write a program to generate points according to a uniform distribution in a unit cube, Generate 104 such points. (b) Write a program to estimate the density at the origin based on your 104 points as a function of the size of a cubical window function of size h. Plot your estimate as a function of h, for (c) Evaluate the density at the origin using n of your points and the volume of a cube window which just encloses n points. Plot your estimate as a function of (d) Write a program to generate 104 points from a spherical Gaussian density (with Σ = I) centered on the origin. Repeat (b) & (c) with your Gaussian data. (e) Discuss any qualitative differences between the functional dependencies of your estimation results for the uniform and Gaussian densities.

Explore some of the properties of density estimation in the following way. (a) Write a program to generate points according to a uniform distribution in a unit cube, Generate 104 such points. (b) Write a program to estimate the density at the origin based on your 104 points as a function of the size of a cubical window function of size h. Plot your estimate as a function of h, for (c) Evaluate the density at the origin using n of your points and the volume of a cube window which just encloses n points. Plot your estimate as a function of (d) Write a program to generate 104 points from a spherical Gaussian density (with Σ = I) centered on the origin. Repeat (b) & (c) with your Gaussian data. (e) Discuss any qualitative differences between the functional dependencies of your estimation results for the uniform and Gaussian densities.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.27P

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