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Normality
Statistical property where a data distribution follows a Gaussian law characterized by its perfect symmetry around the mean and its specific kurtosis.
Kurtosis
Parameter characterizing the concentration of values around the mean, measuring whether the tails of a distribution are thicker (leptokurtic) or flatter (platykurtic) than a normal distribution.
Shapiro-Wilk Test
Powerful statistical hypothesis test for assessing the normality of a sample, particularly effective for small sample sizes (n < 50).
Kolmogorov-Smirnov Test
Non-parametric test comparing the empirical distribution function of a sample to that of a theoretical distribution to determine the fit to this distribution.
Probability Density
Function describing the relative probability density for a continuous random variable, whose integral over an interval gives the probability of observation within that interval.
Cumulative Distribution Function
Cumulative function F(x) giving the probability that a random variable takes a value less than or equal to x, completely characterizing a distribution.
Statistical Moments
Quantitative measures describing the shape of a distribution, including the first moment (mean), the second (variance), the third (skewness), and the fourth (kurtosis).
Standardization
Process transforming variables into Z-scores with a mean of 0 and a standard deviation of 1, facilitating comparison between different distributions.
Leptokurtic Distribution
Distribution with kurtosis greater than that of the normal distribution, featuring thicker tails and a sharper peak, indicating a higher probability of extreme values.
Platykurtic Distribution
Distribution with kurtosis lower than the normal distribution, characterized by a flatter shape and thinner tails compared to the Gaussian distribution.
Jarque-Bera Test
Goodness-of-fit test for normality based on skewness and kurtosis coefficients, particularly suitable for large samples.
Excess Kurtosis
Measure of kurtosis adjusted by subtracting 3 (the kurtosis value for a normal distribution), allowing direct assessment of the deviation in flatness from the normal distribution.
Bimodal Distribution
Distribution exhibiting two distinct modes, suggesting the presence of two subpopulations or different generating mechanisms in the data.
Anderson-Darling Test
Normality test that modifies the Kolmogorov-Smirnov test by giving more weight to the tails of the distribution, increasing its sensitivity to deviations in the tails.