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A lognormal distribution is a continuous probability distribution of a random variable in which logarithm is normally distributed. Thus, if the random variable has a lognormal distribution, then has a normal distribution. Likewise, if has a normal distribution, then has a lognormal distribution.

One key difference between the two is that lognormal distributions contain only positive numbers, whereas normal distribution can contain negative values. Another key difference between the two is the shape of the graph. Normally distributed data forms a symmetric bell-shaped graph, as seen in the previous graphs.

The lognormal distribution differs from the normal distribution in several ways. A major difference is in its shape: the normal distribution is symmetrical, whereas the lognormal distribution is not. Because the values in a lognormal distribution are positive, they create a right-skewed curve.

The lognormal distribution is used to describe load variables, whereas the normal distribution is used to describe resistance variables. However, a variable that is known as never taking on negative values is normally assigned a lognormal distribution rather than a normal distribution.

The lognormal distribution differs from the normal distribution in several ways. A major difference is in its shape: the normal distribution is symmetrical, whereas the lognormal distribution is not. Because the values in a lognormal distribution are positive, they create a right-skewed curve.

Lognormal distribution formulas Mean of the lognormal distribution: exp(? + ?² / 2) Median of the lognormal distribution: exp(?) Mode of the lognormal distribution: exp(? - ?²) Variance of the lognormal distribution: exp(?²) - 1 ? exp(2? + ?²) Skewness of the lognormal distribution: exp(?²) + 2 ? ?exp(?²) - 1

The standard lognormal distribution has a location parameter of 0 and a scale parameter of 1 (shown in blue in the image below).