Parametric and non-parametric statistical methods are two different approaches to analyzing data in statistics and probability theory.
Parametric statistics assumes that the data follows a specific probability distribution, such as the normal distribution or the binomial distribution. This means that the parameters of the distribution can be estimated using the sample data, and the statistical tests can be based on these parameter estimates. For example, if we assume that a set of data follows a normal distribution, we can use the mean and standard deviation of the data to estimate the parameters of the normal distribution, and then use these parameter estimates to conduct hypothesis tests or confidence intervals.
On the other hand, non-parametric statistics does not make any assumptions about the underlying distribution of the data. Instead, it uses statistical methods that are based on ranking or order statistics of the sample data, such as the median or Wilcoxon signed-rank test. Non-parametric methods are often used when the data does not follow a normal distribution, or when the sample size is small and the normal distribution assumption may not be valid.
In general, parametric methods are more powerful and efficient when the assumptions are met, while non-parametric methods are more robust and flexible when the assumptions are not met. For example, if we have a large sample of data that we believe follows a normal distribution, we may choose to use a parametric method such as a t-test or ANOVA. However, if we have a small sample or suspect that the data does not follow a normal distribution, we may choose to use a non-parametric method such as the Wilcoxon rank-sum test or Kruskal-Wallis test.
In quantitative trading/investment, parametric methods are commonly used to model stock prices or financial returns, such as using the normal distribution to model daily stock returns. Non-parametric methods are sometimes used to detect patterns in financial time series data, such as using the Kolmogorov-Smirnov test to test for the presence of trends or cycles.