normalijakautuma
Normalijakautuma, known in Finnish as normaalijakauma, is a continuous probability distribution that is symmetric and bell-shaped. It is fully described by two parameters: the mean μ, which determines the center, and the standard deviation σ > 0, which determines the spread. The probability density function is f(x) = (1/(σ√(2π))) exp(-(x-μ)²/(2σ²)). The cumulative distribution function is F(x) = (1/2)[1 + erf((x-μ)/(σ√2))], where erf denotes the error function.
Key properties include symmetry around μ, zero skewness, and a kurtosis of 3 (excess kurtosis 0). The
Applications include modeling measurement errors, natural phenomena, and various statistical methods that rely on normality assumptions,
Limitations include that real data may deviate from normality, especially for bounded, skewed, or heavy-tailed variables.