Difference Between Normal Distribution and Lognormal Distribution
Characteristic | Normal Distribution | Lognormal Distribution |
---|---|---|
Shape | Symmetrical | Right-skewed |
Range of Values | From negative to positive | From zero to positive |
Parameter Interpretation | Mean (μ) and Standard Deviation (σ) | Mean of ln(x) (μ) and Standard Deviation of ln(x) (σ) |
Data Transformation | Not transformed | Natural logarithm transformation of data |
Applications | Common in many natural phenomena such as heights, weights, IQ scores | Used for data with positive values that exhibit right-skewed patterns, like income, stock prices, and resource reserves |
Real-life Examples | Heights, weights, IQ scores | Stock returns, resource reserves, income distribution |
Probability Density Function | Symmetrical bell-shaped curve | Right-skewed, starts from zero and rises to a peak |
Mean and Variance | Define the central tendency and spread of data | Define the central tendency and spread of the natural logarithm of the data |
Common Parameter Values | μ (mean) and σ (standard deviation) | μ and σ represent parameters of the natural logarithm of the data |
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