**Nonparametric statistics** or distribution-free tests are those that do not rely on

parameter estimates or precise assumptions about the distributions of variables.

Mann-Whitney Test

Wilcoxon’s Matched-Pairs Signed-Ranks Test

Kruskal-Wallis One-Way ANOVA

Friedman’s Rank Test for k Correlated Samples

**A nonparametric model **is one in which the only assumptions made about

the distribution of the observations is that they are independently identically distributed (i.i.d.) from an arbitrary continuous distribution. There are no

parameters in a nonparametric model.

**A semiparametric model** is one in which has parameters but very weak as-

sumptions are made about the actual form of the distribution of the observa-

tions. Both nonparametric and semiparametric models used to be (and often still

are) lumped together and called nonparametric models.

Procedures derived for nonparametric and semiparametric models are often

called robust procedures since they are dependent only on very weak assumption

**A parametric statistical model** is a model whose joint distribution is dependenton several unknown constants called parameters. The only things unknown about the model are the parameters. Two parametric models commonly en-countered in astronomical experiments are

1. The Poisson model in which we assume that the observations are indepen-

dent Poisson random variables with unknown common mean

2. The normal model in which the observations are independently distributed

with unknown mean and unknown variance