Mean and Variance of Lognormal Distribution
Mean (μ)
- The mean (μ) of a lognormal distribution is not simply the mean of the original data; it is the mean of the natural logarithm of the data.
- Then, find the mean of these natural logarithms. Mathematically, μ is the average of ln(x), where x represents the original data.
- The mean of the lognormal distribution is not equivalent to the median or the mode of the original data. It is important to remember that the lognormal distribution models the distribution of the logarithms of the data, which can result in quite different characteristics.
Where,
- μ represents the mean of the natural logarithm of the data.
- σ represents the standard deviation of the natural logarithm of the data.
- e is the mathematical constant approximately equal to 2.71828.
Variance (σ2)
- The variance (σ2) of a lognormal distribution is similarly calculated from the natural logarithms of the data.
- The standard deviation of the natural logarithm of the data is σ. To get the variance, square this standard deviation that will result in σ2.
- The variance formula involves both σ and μ.
- The variance of the lognormal distribution helps describe how data points are dispersed around the mean of the natural logarithm of the data.
Where,
- The standard deviation of the natural logarithm of the data is represented by σ
- The mean of the natural logarithm of the data is represented by μ
- e is the mathematical constant approximately equal to 2.71828.
Lognormal Distribution in Business Statistics
In business statistics, Lognormal Distribution is a crucial probability distribution model as it characterises data with positive values that show right-skewed patterns, which makes it suitable for various real-world scenarios like stock prices, income, resource reserves, social media, etc. Understanding Lognormal Distribution helps in risk assessment, portfolio optimisation, and decision-making in fields, like finance, economics, and resource management.
Table of Content
- Probability Density Function (PDF) of Lognormal Distribution
- Lognormal Distribution Curve
- Mean and Variance of Lognormal Distribution
- Applications of Lognormal Distribution
- Examples of Lognormal Distribution
- Difference Between Normal Distribution and Lognormal Distribution
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