Examples of Lognormal Distribution
Example 1:
The daily website visitors of a small blog follow a lognormal distribution with a mean of 50 visitors and a geometric standard deviation of 1.1. Calculate the variance of the daily website visitors.
Solution:
To find the variance σ2 we will use the formula for the variance of a lognormal distribution:
Accordng to the given information, we have:
- σ2 is the variance
- μ = 50
- σ = 1.1
putting these values in the formula we get,
σ2 = 21.1829
∴ Variance of the daily website visitors is approximately 21.1829.
Example 2:
The population of a village follows a lognormal distribution with a median population of 1,000 and a geometric standard deviation of 1.2. Calculate the mean (average) population of the village.
Solution:
To find the mean population μ, you can use the formula for the mean of a lognormal distribution:
Accordng to the given information, we have:
- μ is the mean you want to find.
- μ’= ln1000
- σ= 1.2
putting these values in the formula we get,
μ = 2051.27
∴ the mean population of the village is approximately 2,051.27.
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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