Non-Parametric statistics are statistics (statistic in the sense of a function on a sample) where it is not assumed that the population fits any parametrized distributions. Non-Parametric statistics are typically applied to populations that take on a ranked order (such as movie reviews receiving one to four stars).
The branch of statistics (in the sense of the field of mathematical science) known as non-parametric statistics is concerned with non-parametric statistical models and non-parametric statistical tests.
Non-parametric models differ from parametric models in that the model structure is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance. Nonparametric models are therefore also called distribution free or parameter-free.
Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the frequency distributions of the variables being assessed. The most frequently used tests include
Nonparametric tests have less power than the appropriate parametric tests, but are more robust when the assumptions underlying the parametric test are not satisfied.

A histogram is a simple nonparametric estimate of a probability distribution
Kernel density estimation provides better estimates of the density than histograms.
Nonparametric regression and semiparametric regression methods have been developed based on kernels, splines, and wavelets.
binomial test
Anderson-Darling test
chi-square test
Cochran's Q
Cohen's kappa
Efron-Petrosian Test
Fisher's exact test
Friedman two-way analysis of variance by ranks
Kendall's tau
Kendall's W
Kolmogorov-Smirnov test
Kruskal-Wallis one-way analysis of variance by ranks
Kuiper's test
Mann-Whitney U or Wilcoxon rank sum test
Maximum parsimony for the development of species relationships using computational phylogenetics
McNemar's test (a special case of the chi-squared test)
median test
Pitman's permutation test
Siegel-Tukey test
Spearman's rank correlation coefficient
Student-Newman-Keuls (SNK) test
Wald-Wolfowitz runs test
Wilcoxon signed-rank test.