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wdlang
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suppose we have many dots on a unit n-sphere
i suspect that they satisfy the uniform distribution
but how to verify this?
i suspect that they satisfy the uniform distribution
but how to verify this?
Eynstone said:Divide the sphere into many parts & count the no. of dots in each part. If they're roughly equal,the distribution is close to being uniform.
A uniform distribution on n-sphere refers to a probability distribution where all points on an n-dimensional sphere have an equal chance of being selected. In other words, the data points are evenly spread out on the surface of the n-sphere.
A uniform distribution on n-sphere can be verified by checking if the data points are evenly spread out on the surface of the n-sphere. This can be done by plotting the data points on a graph and visually inspecting if they are evenly distributed. Additionally, statistical tests like the chi-square test can also be used to verify the uniformity of the distribution.
Verifying a uniform distribution on n-sphere is important because it ensures that the data points are not biased towards a particular region on the n-sphere. This is crucial in many scientific fields, such as physics and genetics, where a uniform distribution is necessary for accurate analysis and conclusions.
Some commonly used methods for generating a uniform distribution on n-sphere include the rejection sampling algorithm, the von Neumann's rejection method, and the Marsaglia's method. These methods involve randomly selecting points on the n-sphere with a specific probability distribution to ensure uniformity.
Yes, a uniform distribution on n-sphere can be verified for any value of n. However, as the number of dimensions increases, it becomes more challenging to visually verify the uniformity of the distribution. In such cases, statistical tests are often used to verify the uniformity of the distribution.