normal distribution

plural normal distributions

1. mathematicsAny of a family of continuous probability distributions such that the probability density function is the Gaussian function

   φ_(μ,σ²)(x)=1/(σ√2π),e²)/(2σ²))=1/σφ((x-μ)/σ), x∈ℝ.

   3 more examples

   It begins with the normal distribution, which is the limiting form of the sample sum over an arbitrary population.

   2008, James L. Johnson, Probability and Statistics for Computer Science, Wiley, page 437

   The normal distribution is the backbone of traditional statistics. We learn very early in our statistics training that the distribution of sample means, regardless of the shape of the parent distribution, approaches a normal distribution as the sample size increases.

   2012, Larry Pace, Beginning R: An Introduction to Statistical Programming, Apress, page 103

   The development of the general theories of the normal distributions began with the work of de Moivre (1733, 1738) in his studies of approximations to certain binomial distributions for large positive integer n > 0.

   2014, Mohammad Ahsanullah, B.M. Golam Kibria, Mohammad Shakil, Normal and Student's t Distributions and Their Applications, Springer (Atlantis Press), page 7

   Synonyms: Gaussian distribution, Gaussian curve, bell curve