Скачать или смотреть Understanding Negative Skewness in Laplace Distribution Sampling with Scipy

Discover the reasons behind negatively skewed densities when sampling from a Laplace distribution using Scipy and learn how to address this issue with practical code examples.
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Understanding Negative Skewness in Laplace Distribution Sampling with Scipy

When working with statistical distributions, particularly the Laplace distribution, you might encounter unexpected results in your data. One common issue is the appearance of negative skewness when drawing samples. This guide aims to clarify why this phenomenon occurs, especially when working with the scipy library in Python, and how to effectively remedy it.

The Problem

In two different examples, draws from a Laplace distribution show a suspicious pattern of negative skewness. Specifically, when the scale of the distribution is derived from distributions with positive values (like Half-Cauchy and Exponential), the resulting empirical distribution consistently leans negatively skewed. According to expectations, one might assume that with a sufficiently large sample size, symmetry would manifest more clearly. However, this is not the case as demonstrated below:

Example 0 Code

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Example 1 Code

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Results from Examples

Both examples produce highly negative mean values and indicate that the quantiles of the distributions are skewed. It raises the question: why does this happen?

The Underlying Cause

The crux of the issue lies in how the random state interacts between the two variables being generated. When using the same random_state argument for both distributions:

The samples generated from the uniform distribution (which underpins all random sampling functions) become correlated.

This correlation creates discerning relationships between the scale parameters given to laplace.rvs() and the uniform samples, resulting in distorted sampling outcomes—with excessive negative values and minor positive values.

The Solution

To correct this issue and realize the expected symmetry in the sampled distribution, consider the following solutions:

1. Use Different random_state Values

Adjust the random_state for the scale and Laplace sampling so they do not interfere with each other. For instance:

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2. Use a Single Random Generator Instance

A preferred method is to establish a single random generator instance and share it across your sampling functions. This ensures that both processes draw from new samples without mutual influence:

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By using the same generator, you will avoid the correlations that lead to negative skewness.

Conclusion

Understanding the interactions between sampling methods and distribution parameters is crucial to achieving accurate statistical results. When utilizing functions like laplace.rvs() within Scipy, be cognizant of how your random state parameters can affect the distribution of your draws. By applying the solutions discussed, you can rectify negative skewness and align your results with the expected symmetry inherent in large samples.

Implementing these insights will significantly enhance your work with probabilistic models, ensuring reliable and valid outcomes when dealing with distributions.