Table of Contents
Logarithmic Normal Distribution
A logarithmic normal distribution is a type of normal distribution that is characterized by a logarithmic scale for the x-axis and a linear scale for the y-axis. This type of distribution is often used to model data that is skewed to the right or to the left.
Log Normal Distribution Definition
A log-normal distribution is a continuous probability distribution that is obtained by taking the natural logarithm of a random variable that is normally distributed.
The log-normal distribution is often used to model the distribution of stock prices, since stock prices tend to follow a log-normal distribution.
How to Find Log – Normal Distribution?
The equation for the normal distribution is:
where is the mean and is the standard deviation.
To find the log of the normal distribution, you first need to find the log of the mean and the log of the standard deviation. Then, you can use the equation for the normal distribution to find the log of the distribution.
Lognormal Distribution Parameters
Mean: μ
Standard deviation: σ
Shape parameter: k
Mean of Lognormal Distribution
The mean of a lognormal distribution is the first moment of the distribution, which is also the mean of the logarithms of the values in the distribution. This means that the mean is equal to the sum of the values in the distribution multiplied by their respective logarithms.
Median of Lognormal Distribution
The median of a lognormal distribution is the value at which the cumulative distribution function is equal to 0.5.
Mode of Lognormal Distribution
The lognormal distribution is a continuous probability distribution that is used to model the behavior of a random variable that is the logarithm of a normally distributed random variable.
Variance of Lognormal Distribution
If we have a lognormal distribution, the standard deviation of the distribution is equal to the root mean square of the natural logarithms of the values in the distribution.
