# What is Lognormal Distribution?

Lognormal distribution is a term used in probability theory and related mathematics. It refers to the probability distribution of a variable with a normally distributed logarithm. It is sometimes also called the Galton distribution.

A normal distribution for a variable is also called a Gaussian distribution. It is a good indicator of probability that uses a cluster of results around a mean average. Ideas like the “Bell curve” are also based on normal distribution, and are used in many different kinds of statistical studies.

A lognormal distribution is said to be useful for a number of independent variables with positive values. This kind of calculation is useful, for example, in financial models where variables need to be multiplied or exponentially projected, or in scientific studies including changing conditions.

The study of a lognormal distribution can use both mean and median averages. It can also be related to functions like a probability density function, that seeks to analyze its formation, and a cumulative distribution function. Statisticians using these kinds of probability theories take advantage of diverse equations in order to learn more about what these projections mean.

Although the normal distribution is attributed to Carl Friedrich Guass, a German scientist who was active in many scientific fields, historians actually credit Abraham de Moivre with the “invention” of this technique. De Moivre, a French mathematician, was a contemporary of Isaac Newton who was famous for his contributions to trigonometry and other types of mathematics. The history of math shows how future engineers and mathematicians built on the pioneering efforts of these early thinkers in order to apply their work to various uses.

These days, industry experts report that lognormal distribution is often useful for modeling the potential failure of a physical unit under stress loads. Engineers use lognormal distribution, as well as another popular method called Weibull distribution, to assess failure probabilities. These two kinds of probability tools are sometimes included in industry-specific software for predictive modeling.

Lognormal distribution is also useful in other studies that some call biological or organic. For example, scientists have shown that the dilution of one liquid into another tends to follow lognormal distribution patterns. The same patterns are evident in other organic events such as the fading of a light source. This makes lognormal distribution valuable in studies of “human and ecological risk assessment” and other similar pursuits, according to expert researchers who use lognormal distributions extensively.

## Discussion Comments

Can anyone help answer this question?

Your supervisor asks you to calculate the design stress for a brittle nickel aluminide rod she wants to use in high temperature application in which the component is always in tension. In tensile testing of the given rods, the results yield an average tensile stress of 673 MPa and Weibull modulus of 14.7. What must be the design stress if 99.999 percent of the rods can be subject to the design stress without fracture?

Everyone knows what a bell curve is. It’s what you hope teachers will grade you with when you otherwise expect to get a failing grade in your statistics class!

Actually the bell curve saved me a few times in college, not only in statistics but in other hard courses. When we all did poorly, the curve had a way of magically transforming my “D” into a “B.”

What was interesting was that later in life after I got married, my wife decided to go back to school. She took some biochemistry classes, and the teacher graded on a curve in that class as well.

However, it was my wife's grades which defined the curve! That is, she usually got close to a 100 on most of her exams. I told her never to divulge that secret to the other students, who may begin to resent her if they did not do well themselves.

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