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Normal

In: Statistical Distributions

Author

Listed:
  • Nick T. Thomopoulos

    (Illinois Institute of Technology, Stuart School of Business)

Abstract

In 1809, Carl Friedrich Gauss introduced the method of least squares, the maximum likelihood estimator method and the normal distribution, which is often referred as the Gaussian distribution. The normal distribution is the most commonly used distribution in all disciplines. Tne normal has a random variable x with two parameters, μ is the mean, and σ is the standard deviation. A related distribution is the standard normal with random variable z whose mean is zero and standard deviation is one. An easy way to convert from x to z and also from z to x is shown. Tables on the standard normal distribution are available in almost all statistics books. There is no closed-form solution to the cumulative probability, denoted as F(z), and thereby various quantitative methods have been developed over the years. This chapter provides the Hasting’s approximation formula to find F(z) from z: and also another Hasting’s approximation formula to find z from F(z). When sample data is available, the sample average and sample standard deviation are used to estimate the mean and standard deviation of the normal. When sample data is not available, a method is shown on how to estimate the mean and standard deviation of the normal from some approximate measures of the distribution.

Suggested Citation

  • Nick T. Thomopoulos, 2017. "Normal," Springer Books, in: Statistical Distributions, chapter 0, pages 69-76, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-65112-5_8
    DOI: 10.1007/978-3-319-65112-5_8
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