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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Probability Density Function (PDF) of Lognormal Distribution

The probability density function (PDF) for the lognormal distribution depends on two parameters, μ (mean) and σ (standard deviation), for x values greater than 0. When we take the logarithm of our lognormal data, μ represents the mean, and σ is the standard deviation of this transformed data....

Lognormal Distribution Curve

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Mean and Variance of Lognormal Distribution

Mean (μ)...

Applications of Lognormal Distribution

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Examples of Lognormal Distribution

Example 1:...

Difference Between Normal Distribution and Lognormal Distribution

Characteristic Normal Distribution Lognormal Distribution ShapeSymmetricalRight-skewedRange of ValuesFrom negative to positiveFrom zero to positiveParameter InterpretationMean (μ) and Standard Deviation (σ)Mean of ln(x) (μ) and Standard Deviation of ln(x) (σ)Data TransformationNot transformedNatural logarithm transformation of dataApplicationsCommon in many natural phenomena such as heights, weights, IQ scoresUsed for data with positive values that exhibit right-skewed patterns, like income, stock prices, and resource reservesReal-life ExamplesHeights, weights, IQ scoresStock returns, resource reserves, income distributionProbability Density FunctionSymmetrical bell-shaped curveRight-skewed, starts from zero and rises to a peakMean and VarianceDefine the central tendency and spread of dataDefine the central tendency and spread of the natural logarithm of the dataCommon Parameter Valuesμ (mean) and σ (standard deviation)μ and σ represent parameters of the natural logarithm of the data...

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