HCq {QSutils} | R Documentation

## Set of functions to compute the Havrda-Charvat estimator

### Description

HCq computes the Havrda-Charvat estimator, and HCqVar computes the Havrda-Charvat asymptotic variance for a given exponent. By using HCqProfile, a Havrda-Charvat estimator is calculated for a predefined vector of exponents to obtain the full profile in the range, 0 to Inf.

### Usage

    HCq(w, q)
    HCqVar(w, q)
    HCqProfile(w, q = NULL)

### Arguments

`w` | Vector of observed counts or frequencies.
`q` | Exponent. By default, a vector of values 1, 2, 3, 4 and Inf.

### Details

In `HCq` only the first element in q is considered. `HCqProfile` is vectorized and considers all elements in q. When q is NULL: in this case, a default vector is taken to obtain the full profile in the range 0 to Inf.

### Value

A value that corresponds to the Havrda-Charvat estimator when `HCq` or `HCqVar` is used. A data frame with the Havrda-Charvat estimator for each exponent when `HCqProfile` is used.

### Author(s)

Mercedes Guerrero-Murillo and Josep Gregori

### References

Gregori J, Perales C, Rodriguez-Frias F, Esteban JI, Quer J, Domingo E. Viral quasispecies complexity measures. Virology. 2016 Jun;493:227-37. doi: 10.1016/j.virol.2016.03.017. Epub 2016 Apr 6. Review. PubMed PMID: 27060566.

Gregori J, Salicrú M, Domingo E, Sanchez A, Esteban JI, Rodríguez-Frías F, Quer J. Inference with viral quasispecies diversity indices: clonal and NGS approaches. Bioinformatics. 2014 Apr 15;30(8):1104-1111. Epub 2014 Jan 2. PubMed PMID: 24389655.

Pavoine, S. (2005). M?thodes statistiques pour la mesure de la biodiversit?. UMR CNRS 5558 Biometrie et Biologie Evolutive.

### See Also

`Hill`, `Renyi`

### Examples

    # A vector of observed counts.
    nr<-c(464, 62, 39, 27, 37, 16, 33, 54, 248, 20)

    # Havrda-Charvat estimator for q=4.
    HCq(nr,4)

    # Havrda-Charvat estimator variance for q=4.
    HCqVar(nr,4)

    # Prolife of Havrda-Charvat estimator for 0:4 and Inf.
    HCqProfile(nr,c(0:4,Inf))

    # Full profile.
    HCqProfile(nr)

[Package QSutils version 1.12.0 Index]