The 2 Parameter Normal Distribution 7 Formulas

The 2 Parameter Normal Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Normal distribution is a continuous distribution widely taught. It is commonly used to describe items, measurements, or time to failure data when there are many additive perturbations that comprise the results. This short article focuses on 7 formulas of the Normal Distribution.

If you want to know more about fitting a set of data to a distribution, well that is in another article.

It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions.

Parameters

The location parameter, μ, is the mean of the distribution. It is the mean, median, and mode, since the distribution is symmetrical about the mean.

The scale parameter is the variance, σ^2, of the distribution, or the square of the standard deviation.

Probability Density Function (PDF)

With -∞ < t < ∞ then the probability density function formula is:

Where 𝜙 is the standard normal pdf with μ = 0 and σ^2 = 1