Density estimation

1. Non-parametric

1.1. Error criteria

1.1.1. mean squared error

1.1.2. L∞, L1, Lk norms

1.1.3. L2 norm: ISE

1.1.4. Mean ISE

1.1.4.1. may emphasize tails or interval

1.1.5. Kullback-Leibler

1.1.6. Hellinger distance

1.1.7. Akaike’s information criterion

1.1.8. ISE/L2E

1.2. Families

1.2.1. Pearson

1.2.2. Johnson

1.2.3. Marshall and Olkin

1.3. Estimators

1.3.1. Empirical CDF

1.3.2. Histogram

1.3.2.1. Bin count

1.3.2.1.1. Sturges

1.3.2.1.2. Doane’s

1.3.2.1.3. Scott’s

1.3.2.1.4. Wand

1.3.2.1.5. Freedman and Diaconis’s

1.3.2.1.6. Duda and Hart

1.3.2.2. Simple

1.3.2.3. Rootgram (Tukey 1977)

1.3.2.4. Frequency polygon

1.3.2.5. Averaged shifted histogram

1.3.3. KERNEL

2. Parametric

3. Graphical

4. Metrics

4.1. Skewness

4.1.1. асимметрия

4.2. Kurtosis

4.2.1. эксце́сс

4.3. heavy-tailed