# Test of CSPR for Dinucleotides Under Gibbs Distribution

### Description

Performs a test of Chargaff's second parity rule (CSPR) for dinucleotides under a Gibbsian assumption on the DNA sequence, which was proposed in Hart and Mart<ed>nez (2012).

### Usage

1 | ```
chargaff.gibbs.test(x, maxLag=200)
``` |

### Arguments

`x` |
either a character vector representing a DNA sequence in which each element contains a single nucleotide, or a DNA sequence stored using the SeqFastadna class from the seqinr package. |

`maxLag` |
The maximum number of lags (cylinder lengths) to use in computing variances. the default value is 200. |

### Details

This function performs a test of Chargaff's second parity rule for dinucleotides
assuming the DNA sequence was generated by a Gibbs distribution. Under the null
hypothesis, the test statistic *eta* is asymptotically
*chi-squared* on 5 degrees of freedom.

The test is set up as follows:

*H0*: the sequence complies with CSPR for dinucleotides

*H1*: the sequence does not comply with CSPR for dinucleotides

### Value

A list with class "htest" containing the following components:

`statistic` |
the value of the test statistic. |

`p.value` |
the p-value of the test. |

`method` |
a character string indicating what type of test was performed. |

`data.name` |
a character string giving the name of the data. |

`FHat` |
the 5-element vector |

`pairs` |
the stochastic matrix of dinucleotide counts used to derive |

`v` |
The asymptotic covariance matrix of |

`n` |
the length of the DNA sequence. |

`cutoff` |
the actual number of lags used by the algorithm to calculate covariances. |

`maxCutoff` |
the value specified for the maxLag parameter when the test was performed. |

### Author(s)

Andrew Hart and Servet Mart<ed>nez

### References

Hart, A.G. and Mart<ed>nez, S. (2012)
A Gibbs approach to Chargaff's second parity rule.
*J. Stat. Phys.* **146(2)**, 408-422.

### See Also

`chargaff0.test`

, `chargaff1.test`

,
`chargaff2.test`

, `agct.test`

,
`ag.test`

### Examples

1 2 3 4 5 6 7 8 9 | ```
#Demonstration on real bacterial sequence
data(nanoarchaeum)
chargaff.gibbs.test(nanoarchaeum)
#Simulate synthetic DNA sequence that does not satisfy Chargaff's second parity rule
trans.mat <- matrix(c(.4, .1, .4, .1, .2, .1, .6, .1, .4, .1, .3, .2, .1, .2, .4, .3),
ncol=4, byrow=TRUE)
seq <- simulateMarkovChain(500000, trans.mat, states=c("a", "c", "g", "t"))
chargaff.gibbs.test(seq)
``` |

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