Normal_Dist Command

The Normal_Dist command visualizes the Normal (Gaussian) distribution through probability and frequency-domain representations. The normal distribution is one of the most important distributions in statistics and forms the foundation of many financial and economic models.

Main idea: understand the bell curve and the probability of observations occurring around an expected value.

Example


Normal_Dist(0,1)

This example displays the standard normal distribution with mean 0 and standard deviation 1.

Output Panels

Probability Density Function (PDF)
Cumulative Distribution Function (CDF)
Characteristic Function (CF)
Characteristic Function Components

Syntax


Normal_Dist(mean,stdDev)

mean – expected value
stdDev – standard deviation

Mathematical Definition


f(x)=1/(σ√(2π))
      exp(-(x-μ)^2/(2σ²))

The Normal distribution is symmetric around its mean and is completely described by its mean and standard deviation.

Applications

Measurement errors
Risk management
Statistical inference
Portfolio analysis
Central Limit Theorem demonstrations

Many statistical techniques assume normally distributed errors, making the Normal distribution one of the most widely used models in quantitative analysis.