# diri.est: Fitting a Dirichlet distribution In Compositional: Compositional Data Analysis

## Description

Estimation of the parameters of a fitted Dirichlet distribution.

## Usage

 `1` ```diri.est(x, type = "mle") ```

## Arguments

 `x` A matrix containing compositional data. `type` If you want to estimate the parameters use type="mle". If you want to estimate the mean vector along with the precision parameter, the second parametrisation of the Dirichlet, use type="prec".

## Details

Maximum likelihood estimation of the parameters of a Dirichlet distribution is performed.

## Value

A list including:

 `loglik` The value of the log-likelihood. `param` The estimated parameters. `phi` The estimated precision parameter, if type = "prec". `a` The estimated mean vector, if type = "prec". `runtime` The run time of the maximisation procedure.

## Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]> and Giorgos Athineou <[email protected]>

## References

Ng Kai Wang, Guo-Liang Tian and Man-Lai Tang (2011). Dirichlet and related distributions: Theory, methods and applications. John Wiley \& Sons.

Aitchison J. (1986). The statistical analysis of compositional data. Chapman \& Hall.

```diri.nr, diri.contour, rdiri, ddiri ```

## Examples

 ```1 2 3``` ```x <- rdiri( 100, c(5, 7, 1, 3, 10, 2, 4) ) diri.est(x) diri.est(x, type = "prec") ```

### Example output

```\$loglik
[1] 1053.32

\$param
[1]  5.3279151  6.9683480  0.9256242  3.2000572 10.5698852  2.1313562  4.2436429

\$std
[1] 0.06866641 0.06694560 0.08706442 0.07289223 0.06487948 0.07714100 0.07039358

\$runtime
user  system elapsed
0.006   0.000   0.012

\$loglik
[1] 1053.32

\$phi
[1] 33.36711

\$a
[1] 0.15967701 0.20884064 0.02774076 0.09590528 0.31677842 0.06387642 0.12718146

\$b
[1]  5.3279604  6.9684086  0.9256292  3.2000822 10.5699806  2.1313717  4.2436780

\$runtime
user  system elapsed
0.012   0.000   0.012
```

Compositional documentation built on June 4, 2018, 5:04 p.m.