How to use the LOGNORM.DIST() function in Excel

This function returns values from the lognormal distribution where the natural logarithm of the random variable follows a normal distribution with parameters μ (mean) and σ (standard_dev). The probability density function (PDF) is given by:

Syntax

LOGNORM.DIST(x; mean; standard_dev; cumulative)

Arguments

• x (required): Evaluation point (x>0x>0)
• mean (required): Mean of ln⁡(x)ln(x) (μμ)
• standard_dev (required): Standard deviation of ln⁡(x)ln(x) (σ>0σ>0)
• cumulative (required):
  • TRUE: Returns cumulative distribution (CDF):

where ΦΦ is the standard normal CDF.

• • FALSE: Returns probability density (PDF)

Background

The lognormal distribution models multiplicative processes where:

1. Skewness: Right-tailed distribution
2. Multiplicative effects: If X=eYX=eY with Y∼N(μ,σ2)Y∼N(μ,σ2), then XX is lognormal
3. Real-world examples:
   • Income distributions (growth rates compound multiplicatively)
   • Particle sizes in aerosols

Key properties:

• Mean: eμ+σ2/2eμ+σ2/2
• Variance: (eσ2−1)e2μ+σ2(eσ2−1)e2μ+σ2

Example Calculation

Given:

• x=4x=4
• μ=3.5μ=3.5
• σ=1.2σ=1.2
• Cumulative = TRUE

Compute F(4;3.5,1.2):

1. Standardize: z=ln⁡(4)−3.51.2≈−0.747z=1.2ln(4)−3.5​≈−0.747
2. Evaluate Φ(−0.747)≈0.039084Φ(−0.747)≈0.039084

Result:
LOGNORM.DIST(4, 3.5, 1.2, TRUE) = 0.039084