Derivation of Johnson Distribution - Get Answers Here

Thread starter Moll22
Start date Jan 31, 2014
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In summary, the Johnson distribution is a continuous probability distribution used for modeling non-normal data. It is derived by transforming a normal distribution through a linear combination of four parameters. The assumptions of the Johnson distribution include a continuous underlying distribution and constant transformation parameters for all observations. It differs from other distributions by its ability to take on a wider range of shapes and its use of four parameters instead of two. The Johnson distribution is commonly used in statistical analysis, financial modeling, and quality control for data that may not follow a normal distribution.

Jan 31, 2014

Moll22

Hi guys.
Could anybody tell me how the Johnson distribution was derived? I have searched the internet but I couldn't find anything useful.
Any suggested links or books will be very useful.

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Feb 1, 2014

Stephen Tashi

Science Advisor

You should specify the formula for the "Johnson distribution" and perhaps someone will know another name for it.

1. What is the Johnson distribution?

The Johnson distribution is a continuous probability distribution that is used to model non-normal data. It has four parameters that allow it to take on a wide range of shapes, including symmetric, skewed, and bimodal distributions.

2. How is the Johnson distribution derived?

The Johnson distribution is derived by transforming a normal distribution into a new distribution that can take on a variety of shapes. This transformation is achieved by applying a linear combination of four parameters to the standard normal distribution.

3. What are the assumptions of the Johnson distribution?

The Johnson distribution assumes that the underlying data follows a continuous distribution, and that the data is transformed to be normally distributed. It also assumes that the transformation parameters are constant for all observations.

4. How is the Johnson distribution different from other distributions?

The Johnson distribution is different from other distributions because it can take on a wider range of shapes, making it more flexible for modeling non-normal data. Additionally, it has four parameters instead of the usual two, which allows for more precise fitting to the data.

5. How is the Johnson distribution used in practice?

The Johnson distribution is commonly used in statistical analysis, particularly for fitting data that does not follow a normal distribution. It is also used in financial modeling and in quality control to analyze data that may have non-normal distributions.