# How do you find the mean of a lognormal distribution?

## How do you find the mean of a lognormal distribution?

The mean of the log-normal distribution is m = e μ + σ 2 2 , m = e^{\mu+\frac{\sigma^2}{2}}, m=eμ+2σ2​, which also means that μ \mu μ can be calculated from m m m: μ = ln ⁡ m − 1 2 σ 2 .

## How do you find lognormal?

Lognormal distribution formulas

1. Mean of the lognormal distribution: exp(μ + σ² / 2)
2. Median of the lognormal distribution: exp(μ)
3. Mode of the lognormal distribution: exp(μ – σ²)
4. Variance of the lognormal distribution: [exp(σ²) – 1] ⋅ exp(2μ + σ²)
5. Skewness of the lognormal distribution: [exp(σ²) + 2] ⋅ √[exp(σ²) – 1]

What is the mean and variance of lognormal distribution?

The lognormal distribution is a probability distribution whose logarithm has a normal distribution. The mean m and variance v of a lognormal random variable are functions of the lognormal distribution parameters µ and σ: m = exp ( μ + σ 2 / 2 ) v = exp ( 2 μ + σ 2 ) ( exp ( σ 2 ) − 1 )

What is a lognormal distribution?

From Wikipedia, the free encyclopedia In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution.

### What does log normal mean in statistics?

Log-normal. In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution.

### How do you find the log of a normal distribution?

The term “log-normal” comes from the result of taking the logarithm of both sides: \\log X = \\mu +\\sigma Z. logX = μ+σZ. X X is normally distributed (hence the term log-normal).

What is the moment generating function of the log-normal distribution?

The log-normal distribution does not possess the moment generating function . A closed formula for the characteristic function of a log-normal random variable is not known. The distribution function of a log-normal random variable can be expressed as where is the distribution function of a standard normal random variable.