Which distribution is associated with the term contaminated normal distribution?

Which distribution is associated with the term contaminated normal distribution?

• A. Mixed normal distribution
• B. Contaminated normal distribution
• C. Normal distribution
• D. Skewed distribution

Answer: (B)

The idea being tested is modeling data that are mostly normal but include a few outliers by using a two-component normal mixture. In a contaminated normal model, most observations come from a primary normal distribution with mean μ and variance σ^2, while a small fraction ε come from a second normal distribution with its own mean and variance (often with a larger variance or a different mean). This creates a distribution that looks normal for the bulk of the data but has heavier tails due to the contaminating component, which is exactly what the term “contaminated normal distribution” describes. It’s a specific, two-component case used in robust statistics to account for outliers, unlike a single normal distribution, a skewed distribution, or a general mixed normal model (which could involve more components or different mixing).

The idea being tested is modeling data that are mostly normal but include a few outliers by using a two-component normal mixture. In a contaminated normal model, most observations come from a primary normal distribution with mean μ and variance σ^2, while a small fraction ε come from a second normal distribution with its own mean and variance (often with a larger variance or a different mean). This creates a distribution that looks normal for the bulk of the data but has heavier tails due to the contaminating component, which is exactly what the term “contaminated normal distribution” describes. It’s a specific, two-component case used in robust statistics to account for outliers, unlike a single normal distribution, a skewed distribution, or a general mixed normal model (which could involve more components or different mixing).