inverse.simpson: Distribution evaluation.
In tcR: Advanced Data Analysis of Immune Receptor Repertoires

Description Usage Arguments Value See Also Examples

Functions for evaluating the diversity of species or objects in the given distribution. See the repOverlap function for working with clonesets and a general interface to all of this functions.

Warning! Functions will check if .data is a distribution of a random variable (sum == 1) or not. To force normalisation and / or to prevent this, set .do.norm to TRUE (do normalisation) or FALSE (don't do normalisation), respectively.

- True diversity, or the effective number of types, refers to the number of equally-abundant types needed for the average proportional abundance of the types to equal that observed in the dataset of interest where all types may not be equally abundant.

- Inverse Simpson index is the effective number of types that is obtained when the weighted arithmetic mean is used to quantify average proportional abundance of types in the dataset of interest.

- The Gini coefficient measures the inequality among values of a frequency distribution (for example levels of income). A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income). A Gini coefficient of one (or 100 percents ) expresses maximal inequality among values (for example where only one person has all the income).

- The Gini-Simpson index is the probability of interspecific encounter, i.e., probability that two entities represent different types.

- Chao1 estimator is a nonparameteric asymptotic estimator of species richness (number of species in a population).

inverse.simpson(.data, .do.norm = NA, .laplace = 0)

diversity(.data, .q = 5, .do.norm = NA, .laplace = 0)

gini(.data, .do.norm = NA, .laplace = 0)

gini.simpson(.data, .do.norm = NA, .laplace = 0)

chao1(.data)

`.data`	Numeric vector of values for proportions or for numbers of individuals.
`.do.norm`	One of the three values - NA, T or F. If NA than check for distrubution (sum(.data) == 1) and normalise if needed with the given laplace correction value. if T then do normalisation and laplace correction. If F than don't do normalisaton and laplace correction.
`.laplace`	Value for Laplace correction which will be added to every value in the .data.
`.q`	q-parameter for the Diversity index.

Numeric vector of length 1 with value for all functions except chao1, which returns 4 values: estimated number of species, standart deviation of this number and two 95

repOverlap, entropy, similarity

data(twb)
# Next two are equal calls:
stopifnot(gini(twb[[1]]$Read.count, TRUE, 0) - 0.7609971 < 1e-07)
stopifnot(gini(twb[[1]]$Read.proportion, FALSE) - 0.7609971 < 1e-07)
stopifnot(chao1(twb[[1]]$Read.count)[1] == 1e+04)