View source: R/ddchisqsympar.R

ddchisqsympar | R Documentation |

Symmetrized chi-squared 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.

```
ddchisqsympar(p1, p2)
```

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

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

The chi-squared distance between two discrete distributions `p_1`

and `p_2`

is given by:

`\sum_x{(p_1(x) - p_2(x))^2}/p_2(x)`

Then the symmetrized chi-squared distance is given by the formula:

`||p_1 - p_2|| = \sum_x{(p_1(x) - p_2(x))^2}/(p_1(x) + p_2(x))`

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

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

`ddchisqsym`

: chi-squared distance between two estimated discrete distributions, given samples.

Other distances: `ddhellingerpar`

, `ddjeffreyspar`

, `ddjensenpar`

, `ddlppar`

.

```
# 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")))
ddchisqsympar(p1, p2)
# 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)
ddchisqsympar(p1, p2)
```

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