rightskewed

Right-skewed, or positively skewed, describes a probability distribution in which the right tail is longer or fatter than the left tail. In such distributions, most observations cluster near the lower end, with a tail extending toward higher values.

Common characteristics include a mean that exceeds the median, which in turn exceeds the mode (mean > median > mode). The skewness of the distribution is positive, typically measured by a moment-based coefficient. Right-skewed shapes frequently arise when the variable is bounded below (often at zero) but can take large values, producing occasional extreme high observations.

Right-skewed distributions appear in many real-world contexts, such as income, wealth, city populations, waiting times, and time-to-failure data. They are common in nonnegative data and in processes that accumulate additive positive shocks or multiplicative effects.

Statistical implications include sensitivity of the mean to extreme values and potential misinterpretation of symmetry-based assumptions. Analysts often use the median or other robust statistics to summarize central tendency. Data transformations, particularly logarithmic or Box-Cox transformations, can reduce skewness and improve model fit. When modeling right-skewed data, distributions such as the lognormal, exponential, gamma, or chi-square are frequently appropriate, and generalized linear models with appropriate link functions may be used.

Limitations include scale dependence of skewness and the fact that skewness measures can be unstable with small samples. The presence of right skew does not specify a unique distribution, only a general shape, so distribution fitting and diagnostic checks are important for accurate analysis.