ddlppar | R Documentation |

`L^p`

distance between two discrete probability distributions on the same support (which can be a Cartesian product of `q`

sets) , given the probabilities of the states (which are `q`

-tuples) of the support.

```
ddlppar(p1, p2, p = 1)
```

`p1` |
array (or table) the dimension of which is |

`p2` |
array (or table) the dimension of which is |

`p` |
integer. Parameter of the distance. |

The `L^p`

distance `||p_1 - p_2||`

between two discrete distributions `p_1`

and `p_2`

is given by the formula:

`||p_1 - p_2||^p = \sum_x{|p_1(x)-p_2(x)|^p}`

If `p=1`

, it is the variational distance.

If `p=2`

, it is the Patrick-Fisher distance.

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Sabine Demotes-Mainard

Deza, M.M. and Deza E. (2013). Encyclopedia of distances. Springer.

`ddlp`

: `L^p`

distance between two estimated discrete distributions, given samples.

Other distances: `ddchisqsympar`

, `ddhellingerpar`

, `ddjeffreyspar`

, `ddjensenpar`

.

```
# Example 1
p1 <- array(c(1/2, 1/2), dimnames = list(c("a", "b")))
p2 <- array(c(1/4, 3/4), dimnames = list(c("a", "b")))
ddlppar(p1, p2)
ddlppar(p1, p2, p=2)
# Example 2
x1 <- data.frame(x = factor(c("A", "A", "A", "B", "B", "B")),
y = factor(c("a", "a", "a", "b", "b", "b")))
x2 <- data.frame(x = factor(c("A", "A", "A", "B", "B")),
y = factor(c("a", "a", "b", "a", "b")))
p1 <- table(x1)/nrow(x1)
p2 <- table(x2)/nrow(x2)
ddlppar(p1, p2)
```

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