Welcome to Stats & Stuff, a webapp that allows one to visualise a variety of basic statistical distributions.

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Distributions

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This page is used to visualise the probability functions of a variety of distributions and the convolution of two random variables. The convolution can be specified as a sum or a product of the variables. The joint functions can then be viewed in an approximation of the supported region.

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The Law of Large Numbers

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Demonstrations of the application of the law of large numbers to the binomial distribution. The demonstrations cover the cases where a normal and Poisson distribution can be used to approximate the binomial distribution.

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Create Samples

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Generates a custom dataset based on the user’s choice of distributions. It can be used to generate up to two variables with an option to view a joint histogram. This can be downloaded in the .csv format for personal use.

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Glossary of figures available

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• PMF: Probability Mass Function. A function for discrete variables that returns the probability of a given event occurring.
• PDF: Probability Density Function. This is analogous to the PMF for continuous variables; however, it indicates the probability density, not the probability of a given outcome.
• CDF: Cumulative Density Function. This returns the cumulative probability for a given input, i.e. the probability the variable will be less than the input value.

For the discrete case, the CDF function sums over all values of the PMF up to the input. For the continuous case, it integrates the variable's PDF over the region to the input value.

• Supported region: Shows the values a given distribution can occupy with a non-zero probability.
• Joint Probability Functions: The multidimensional case of the PDF and CDF. This website supports up to 2 independent variables. The PDF is a product of each variable's PMF/PDF.

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